I don't know the activation energy, so I can't give you an Arrhenius plot, but if you assume the reaction rate doubles every 10°C, I know from military experiments that 18 months at 140°F (60°C) can cause ball powder to break down, so if we come down to 20°C (68°F) we would have a time increase of 2⁴×18 months or 288 months or 24 years. I know the military will store double-base ball powders in bunkers sunk into the ground at temperatures in that range, and they put a 20-year limit on it, so it must be about right for that. They put a 45 years limit on single-base powder, so it must deteriorate a little less than half as fast. The bottom line, though, is if you put it in a chest freezer at -20°F (-28.9°C), the trendline says you get 711 years out of the ball powder.
I've had powders go bad in three instances over the years. None resulted in self-ignition. My guess is that requires large masses that self-insulate well enough to get very warm in the center. Either that or, in the case of the double-base powders, enough nitroglycerin weeps out and accumulates somewhere to go off spontaneously, which I understand nitro can do in an acidic environment.