As long as you're not storing them in a swamp or on the surface of the sun, you're pretty much good to go. Ammo is NOT as perishable as some think. It is suceptible to moisture/corrosion, but a few dessicant packs or dehumidified room easily takes care of the worst of it if your climate is a wet one.
And as for heat - well, they don't ship all the ammo our troops are using in the sandbox over to them in air conditioned containers, do they? It would take a fair amount of heat to damage rounds to the point where they'd spontaneously cook off or otherwise be damaged in a serious way.
