Prioritize low humidity, for sure. This is the reason old airplanes are stored in the desert. Humidity and metals really do not get along. The attic is a far better choice than the basement. Cycling high heat will definitely destroy leather saddles and rubber things like tires, but you've figured that out already. Take 'em off.

(As an aside, the opposite holds true for guitars, speaking of musicians. Don't put grandpa's Martin in the attic... )