I went to school in Ithaca, so I think I know the climate pretty well.

It's really only warm enough to matter for a couple of months in the summer. Small, gradual temperature changes aren't too bad, you just want to avoid rapid ones, as those can stress out the wrappers.

I think the wire shelves should be okay, because you can always remove them if you find cigar boxes that are the right size. You could also break some down and lay the pieces on top of the wire shelves.

It should work, because they're designed to hold a temperature and be airtight.