I've said it before and I'll say it again, I think some people worry way too much about the way climate affects ammunition and components. Of course, reloading is a hobby where a little over-cautiuosness is necessary, so I don't blame anyone for taking this or that measure to ensure everything goes off without a hitch - can't hurt, that's for sure.
What I can say is that I've fired reloads from the '70s that were kept in cardboard boxes in a garage that fluctuated between extreme heat and humidity and extreme cold and dryness (so it goes here in the heartland) for their entire existence, and aside from a little discoloration of the cases, there was no difference to speak of between those and something I would load today. I keep all of my components and ammo in a similar garage and I have never had an issue with them. I wouldn't store ammo I intend to use for self defense long term in this way probably, but then again I wouldn't use old ammo for that anyway. Everything else, I wouldn't think twice about. But to each their own, like I said it definitely can't hurt.