I agree with the statements here - that black powder does not deteriorate just because of time.
But the thing you need to avoid with BP is moisture, not heat! BP is just a physical mixture of charcoal, potassium nitrate, and sulfur. Exposing this mixture to heat does not harm it in the least (unless it ignites!)
Smokeless is just the opposite - it does not attract moisture anywhere near as much as black, but heat can cause it to slowly break down.