I think the problem is not the heat but the possibility of humidity. Perhaps you can include something in the case (similar to the idea of the little silica packets in shoe boxes) to absorb any moisture. Check with a local hardware store and see what the have. Also, if you can open up the plastic container every once in awhile to let it breathe. I keep some fabric stored in large plastic bins in a storage shed and once a month I open the tops. Fabric I have been working with I keep in cardboard because of the moisture it may have collected from handling. I asked for a bunch of medium size pizza boxes from a local business and use them to store orphan blocks. The are perfect size, breathe, stack well and I can write on the outside the type of block (Christmas, black/white, etc). But. I don't think just the heat of a couple months would do any real damage. Good luck with the move!