When you say mini fridge do you mean the beer/wine cooler type, usually glass fronted? Its just that I've sern some tiny novelty fridges recently that would be entirely unsuitable.
With the cooler types, they can hold a stable tempersture but set them up well in advance. Opening the door once a day allows sufficient air circulation or you can have a small aquarium pump pumping air into the fridge constantly if you prefer. Hibernating tortoises habe a very low oxygen requirement and their respiration rate is much reduced.