This article is based on a personal opinion, and is not the only opinion out there. It is based on current knowledge at the time of writing, and is backed up by the research of many other authors. However, you should do your own research. The information here is primarily based on the British Isles.
See further information about how to care for a Mediterranean tortoise.
It is important to note that this is not a reflection of the current responsible trade. But it is a history that should help to explain why the older approaches were used.
In the past, tortoises were treated extremely poorly by the old tortoise trade. Tortoises were collected from the wild in their natural countries. Often they were the largest and most impressive animals the collectors could find, which had already survived the trials of the wild and grown under natural sunshine. They were put into packing crates on ships in vast numbers. The ones that survived the journey were then unpacked here in the UK, and sold on market stalls by market traders, among their other products. They were sold to unsuspecting owners without any good advice on their care. The majority were put into a British garden, and forced to endure the harsh weather, and relative lack of sunlight. A very large percentage died within their first few years in Britain.
These were animals taken from their natural habitat which they were adapted to, hot countries around the Mediterranean, and then forced to endure our cold, wet, and poorly sunlit islands. They needed UVB to survive, and the only effective source of it was the sun, so the tortoises had to live outside in a British garden. Each year, the long British winters would force them to undergo a correspondingly long hibernation, with precious little time in between to grow, find food, and absorb enough sunlight. Animals whose lifespan would have been 100 to 150 years in the wild, were frequently reduced to a year or so in the British climate. Occasionally, one would make it to 30, or sometimes 60 (ages were not really recorded, people often made guesses and then stated that as fact), and so people would assume that since a handful survived, it must be OK to keep them this way.
Several species were driven towards extinction by this outdated approach, and the sale of many species was temporarily banned in 1984 to prevent them from becoming extinct. We should not use this old trade, and harmful approach to pet keeping, as a template for how to keep them now.
Captive breeding programmes were set up to replace the wild collecting, and to restock the wild populations. Knowledge of tortoise care was improved dramatically, and UV lighting was developed, allowing them to live indoors with artificial sunlight whenever the garden could not provide for them. The ban on sales was replaced with a licensing system mandating that all pet tortoises of certain species must be registered (and microchipped depending on their size) before they could be sold, and must be sourced legally from a captive breeding programme. Appropriate care regimes were developed based on the updated knowledge and availability of UV lighting. This combination of factors dramatically improved the success rate, so that the vast majority of pet tortoises now survive.
Pet shops are regulated, and there are good shops with knowledgeable staff that can offer assistance and advice. Market stalls have not been allowed to sell pet tortoises or other animals since 1983. Tortoises sold in reputable pet shops are almost always sourced via legitimate channels. Some go out of their way to select tortoises from the best possible stocks, with the best possible upbringing (natural sunshine in the Mediterranean, or effective artificial sunshine). Where required, they are sold with the legal paperwork proving that they are legitimate. Good importers and suppliers try hard to ensure that the animals come from captive breeding programmes by reputable breeders. There are groups who try to ensure that smuggled animals do not enter the EU pet trade and get registered as if they were captive bred animals, as for some years this was a problem. The modern pet trade is nothing like the old trade.
Private breeders may also follow these principles, and there are many excellent breeders who have updated their approaches as new knowledge and UV lighting became available. However, there are still some who keep their tortoises the old way, and breed them because they happen to be living together in a garden. The offspring may be raised the modern way or the old way, and developmental problems can be seen in some cases if good care regimes have not been followed. Paperwork is still legally required for protected species.
The old trade continues in some countries with street sellers trying to convince tourists that it is OK for them to take a wild-caught tortoise home - it is illegal for protected species and carries very stiff penalties.
Reptiles, including tortoises, do not hibernate. They brumate. Hibernation is what some mammals do. Brumation is less of a complete shutdown, and more of a slow-down. Animals that brumate sleep for very lengthy periods, eat less or starve completely. They may wake up to have a drink. With mammals that hibernate, it is often essential to their wellbeing. This does not apply to reptiles, because reptiles do not hibernate.
However, when talking about tortoises, it is common for people to call it hibernation instead of the more correct term. Therefore the rest of this article will refer to it as hibernation.
The majority of tortoise species are incapable of hibernation, and will die if subjected to it. In nature, some species of tortoise hibernate during their winter, if the location they are living in is cold enough that particular year. Examples include the Hermann's tortoise, the Mediterranean spur-thighed tortoise (also known as the Greek tortoise even though it lives in many other Mediterranean countries), and the marginated tortoise. Whether or not they hibernate will depend on the weather that year in the tortoise's territory, and it is possible for an individual tortoise never to hibernate, or to only hibernate once a decade. Hibernation, when it happens, would typically be for only a few weeks, maybe 6 to 10.
In Britain, the winters are far too long, and too frequent. Every year, a tortoise kept outdoors may need to hibernate for 5 months or more (as well as refusing food for a month or so either side). This means that each year, the tortoise desperately tries to find enough resources to survive a hibernation far longer than it naturally would have. Many tortoises are killed by a hibernation that ended up too long.
Some individual tortoises may hibernate in nature, but they do so because unfavourable conditions give them no option. They have to hibernate in order to survive. Tortoise hibernation is the last resort of a desperate animal, when the conditions give it no alternative. It slows down its metabolism, hoping that the favourable conditions will return before it runs out of resources. If the tortoise has favourable conditions during the winter, it would not hibernate.
There are still many sources that state that these tortoises all hibernate every year, but these sources never give detailed studies over multiple extensive areas and multiple years. They ignore the populations of these tortoises that never hibernate because they live in a warmer area. There are highly regarded sources that still talk about hibernation like it is an essential thing, which may be because they do not want to offend the large number of tortoise keepers that have always done it that way. But there are also many sources that state that tortoises do not need to hibernate in order to remain healthy.
Virtually all sources, even the ones advocating hibernation, state that tortoises must not be hibernated if they are at all unwell, and that they should be "overwintered" (kept indoors with artificial sunlight) instead. If they do not need to hibernate when they are unwell and can be overwintered, then there should need to be some compelling reason why they would need to hibernate when they are healthy.
Some sources state that once a tortoise reaches a certain age, it can then somehow cope with Britain, and live outdoors. This is simply nonsense; there is no age at which a tortoise from another climate can suddenly become adapted to the British climate. They have never been adapted to it, which is why they are not naturally found in Britain. Some sources state that the tortoise will tell its owners when it is time to hibernate, by refusing food and sleeping all day. If a tortoise is preparing to hibernate, it is because it is being subjected to unfavourable conditions. The conditions need to be corrected by providing a favourable amount of heat and artificial sunlight, not made worse so that the tortoise is forced to hibernate.
The legacy of historical approaches has shaped the way that tortoises are kept today, in spite of the advances in technology which can keep conditions favourable for the tortoise. Some keepers of older tortoises may continue to hibernate them simply because they do not want to change their tortoise's regime, or their tortoise may continue to do so out of habit, after having had to do so for so many years. Some sources state that they should hibernate because "they do in the wild", but just because an animal may become desperate occasionally in the wild, doesn't mean that it needs to become desperate when kept as a pet. Animals die in the wild too.
An argument that may be heard is that hibernation may have some unknown benifit, and therefore it should be done just in case it is important. While it is true that we do not conclusively know if it has some important benefit, we do know that it has some severe detrimental risks, which can be clearly seen by the number of tortoises that fail to make it through a hibernation. It would be difficult for an unknown benefit to outweigh that.
Hibernation carries a massive risk. The tortoise may run out of energy or water reserves and die. The tortoise may get frostbite and lose a leg or die. The tortoise may get an infection and be unable to fight it since their immune system shuts down during hibernation. Tortoises may be attacked by animals while they are unable to defend themselves. Far too many owners lose their tortoise during hibernation. Maybe it survives the first few years (or the first decade's worth), but then it finally goes too far wrong, and the animal dies. Even when hibernated in ideal conditions with the best possible approach, a significant percentage will die anyway. In cases where the hibernation does not result in death, some tortoises take several months to recover afterwards.
Thriving natural populations (of species that can hibernate) exist that have never needed to hibernate. They reproduce, grow, and live well, all without hibernating. The conditions are favourable to the tortoise, so they do not hibernate. If these conditions are provided for pets, then the pets also should not need to hibernate.
There are two minor benefits to hibernation. It can help get their reproductive cycles into sync with each other. This is primarily only of interest to breeders, and even then, tortoises are successfully bred without requiring hibernation. Hibernation may also help reduce instances of obesity. Obesity occurs because of overfeeding or feeding of inappropriate food. It should be avoided by giving an appropriate diet and appropriate exercise, not by exposing an animal to the risks of a hibernation. These small benefits (which do not relate to many tortoises anyway) are outweighed by the very serious risks.
Hibernation should not be done out of curiosity or for the sake of facing a challenge. It should only be considered if it benefits the animal in a way that outweighs the risks it faces as a result of it.
You are welcome to your own opinion, and no doubt you will be able to find someone to back it up, just as there are people who back up the opinions stated here. However, you should treat any statement of "all of this species hibernate in the wild, so they should hibernate in captivity" as suspect, because it is a blanket statement which ignores the reality that they do not all hibernate, or do not hibernate every year. The reality is a lot more complicated. Do your own research, and decide for yourself. Above all, be prepared to change your approach if compelling medical evidence shows that the approach is harmful or carries unnecessary serious risks.
So you have decided to take the risk and hibernate them anyway. Hibernation happens when the temperatures are cold (between 5 and 10°C, 41 and 50°F, preferably 5°C, 41°F), not when they are warm. Putting them somewhere warm like an airing cupboard means that they are kept awake, and being starved to death. This mistake was made far too many times due to the influence of mistaken old advice. Putting them in a place where the temperature fluctuates, like a cupboard under the stairs, will cause them to wake whenever it gets a bit warm, and sleep whenever it gets cold, wasting energy, and increasing the risk of dying. Places that can approach or drop below freezing (like a garage) will cause frostbite or death - an insulated, ventillated box ("the box method") cannot reliably prevent this. Constantly cold places like old stone houses with no central heating can work, but most of us live in insulated houses that are kept warm. Tortoises may be left to hibernate by digging a burrow in the garden, but they are adapted to doing this in their natural countries, not Britain. If anything goes wrong, the owner will not know, since the tortoise cannot be monitored. The length of hibernation cannot be controlled, and will end up far too long compared with a natural hibernation. They are vulnerable to predators such as foxes. Rats may burrow and encounter the tortoise, and start eating it. None of these approaches are recommended.
A fridge is the only place that stays controllably cold. Therefore a fridge is the recommended approach. The fridge must not be placed in a location that drops below freezing, because fridges can only make things colder, not warmer. It needs low-flow ventillation pipes to be inserted through the rubber seal (optionally with an aquarium air pump providing airflow, but this is not essential), and a clear glass door allows the tortoise to be visually monitored. A small drinks chiller fridge is normally best (without a freezer section). The tortoise needs to be placed in a small, ventillated plastic box inside the fridge so that it can wake and move around a little. The box should be kept away from the chiller surface inside the fridge - usually the top or back wall - as that can be colder than the air in the fridge. It helps to have several bottles full of water in the fridge, which hold the temperature more steady and quickly correct any little fluctuations whenever the door is opened. Practice by "hibernating" an empty box with multiple thermometers to monitor its temperature for an entire winter, before entrusting your pet to this for its brief hibernation the next year. Thermometers need to record the maximum and minimum temperatures they experience, since they cannot be manually monitored constantly.
The tortoise must be a species (and subspecies) that is capable of hibernation. Ideally it should be over 6 years old so that it is strong enough to survive small mistakes. It should have a health check from a specialist first to make sure it has enough resources, and is not ill. The Jackson ratio can be used for some species to get an idea of whether the tortoise is underweight. Hibernation lengths should not exceed the natural hibernation length for that tortoise species, such as 6 weeks. Stop feeding for 6 weeks prior to hibernation to empty the gut and prevent complications from rotting, undigested food. The temperature in the tortoise's enclosure should be lowered over the last 2 weeks. The tortoise must continue to drink, but must not have urinated after its last drink prior to hibernation. After a final health check, it is entrusted to the hibernation fridge, and the max/min temperature and tortoise must be monitored carefully every day. It needs to be weighed every few days to check that it is not losing more than the equivalent of 1 or 2% of its body weight per month. It needs to be brought out of hibernation early if anything goes wrong, such as urination, infection, significant temperature fluctuations, frostbite, or losing more weight than expected. When waking it from hibernation, it should be taken out of the fridge and warmed with artificial sunlight over the course of a few hours, then given baths with dedicated reptile electrolytes. Within a day or two, it must be provided lots of hydration food (fresh, moist leaves) and should start eating. Veterinary care should be sought urgently if it has not eaten within 3 days of waking.
There are services that can hibernate tortoises, which may be offered for a fee, or for a suggested donation, or sometimes for free. Advice about the necessity of hibernation should ideally not come from a source that uses hibernation services as a revenue stream, to remove the possibility of bias.