It might be a bit drafty in a rabbit hutch.. can you post pictures of how you are adapting it to suit a tortoise? How about using a large rubbermaid container with a screened top on it?
There are some critter cages that rabbits use that are very much like a rubbermaid.. has the solid plastic bottom with the cage .. is that they type you are talking about?
I was picturing the wooden rabbit hutch with the chicken wire sides and wire bottom..