I have been cautioned in a permit class that stowing a loaded gun in the glove box or console is a possible issue if I leave the gun and passengers, all of whom have no permits, in the car for an errand. The permitless passengers then become in possession of an illegal loaded firearm in a vehicle. This is an actual consideration at the post office. The who and how of such possibilities becoming a problem in my life are negligible, YMMV.
I would not worry about the thermal considerations. High heat cycles will probably shorten the "shelf life" of your carry ammo, but we are cautioned to shoot up and replace carry ammo for other reasons as well. Mine goes down range at roughly two years.