My Dad brought some .45 ACP back from Europe in 1945.
Since then it has been stored in one house, or another, in:
upstate New York,
Nevada, and now
some with air conditioning, some not (more without).
I still have some - and, the last time any was taken to the range (maybe 5-6 years ago) - it worked just fine.
When I was in the army in the early 60's I acquired some .45 blanks that we used for training our dogs. I gave those to my Dad since he had the pistol at that time - it, too, still works just as good as ever. Again, no particular consideration given to storage conditions, just kept in one house or another and protected from unusual conditions. It could have, upon occasion, seen temperatures below freezing or up to (or, even slightly above) 120+ degrees - but, without any exposure to water, fire, etc. Not in sealed containers, not climate controlled (other than in house, garage, or trailer).
I'm not one to be too concerned about ammo storage conditions. That said, I also don't use any of that ammo for self-defense purposes.
I also have some period correct ammo (in its original packaging) for a 1922 vintage Winchester Model '92 in .25-20. That ammo, like the remainder of the WWII .45 ACP, is not kept for use; but for collectible and/or display purposes with the appropriate firearms. Similarly, I have some old J.C. Higgins, Western Auto, and other manufacturer's, .22 LR ammo for an old Marlin Model 80C, bolt action, that is old enough that it doesn't have a serial number. That was my 'learn to shoot and hunt' rifle that I grew up carrying almost everyday during the summer (no school) months.