Low explosives like BP, Pyrodex and T7 are generally comfortable in the same sorts of places you might be comfortable. I.e.: damp places and hot places are not good places to take naps or store powder. So, the bedroom closet or the man cave are probably good storage locations, the attic and the basement, not so much.
Probably the worst possible danger to your powder is a group of unsupervised children, most likely not your own children, but the children of the liberals who live next door who think it would be cool to blow something up like they see on (name least favorite video game).