OMG a tortoise in the fridge!!! I had a tortoise for nearly 40 years before I lost her and I was devastated as she was so tame. Unfortunately she came out of hibernation with mouth rot, and after being tube fed at the vets for a few weeks she died and feel this was partly due to the fact that she kept waking up during the winter wanting to be fed. I had had to keep her in the kitchen as the unheated spare bedroom, where historically she had been kept was being used.
However, having said that, as long as the frost doesnt get to her, you could put her box inside another box and between the two place polysterene tiles or similar and she should be fine, unless you can use an unheated room in the house which had always worked well for us as at least we knew when she woke up. Ours used to scratch the box like mad, and if we didnt get her out she would climb the sides and one day we found her in her box upside down, so were lucky we got to her. Some people use the garage if it is attached to the house as that is relatively frost free, but problem with that is if you use it for the car the car fumes can kill them. Something else I was told was to cover them with a towel or old blanket as hay/straw contains bacteria and mites etc, which can spread disease.
I found the British Chelonia tortoise rescue group very helpful when my tortoise was ill
http://www.britishcheloniagroup.org.uk/