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If you keep up with the little stuff (pick up food remains, droppings, etc.), you won't need to do a huge cleaning very often...maybe every several months. I've heard that some people go years even. I got my first T in April of this year and have not had to do anything major since then. If you have a T that requires wet sub (babies, swamp dwellers), you will probably need to change it periodically to avoid mold and mites.
Any safe container will do for temporary housing as you clean. It should have a secure lid.
You can also do a yearly monsoon, wet the entire habitat, then introduce a handful of isopods. They will do a very thorough clean up job for you. The moisture will be enough to keep them going for a few weeks.