Feed is in rodent proof metal trash cans with lids. I do leave feed in a hanging feeder which is probably why I found the drowned mouse/pack rat a month ago (mid winter).
If your concrete floor is not in the sun it should stay cooler.
When we rebuilt an abandoned coop we poured a concrete foundation and had a couple courses of CMU (concrete block). Then stick framed above that. The floor inside is dirt with thick layer of straw. The roost is up about 3 feet over...