I'm not a chemical engineer, but I do some work with explosives. There are energetic materials that do not stand up well to frequent cycling between hot and cold, some are resistant to moisture, others are not, and others have narrow temperature range limitations. Modern propellants have similar chemical properties, and like explosives they release huge volumes of gas although they do so without the creation of a shock wave which is the defining property of a high explosive.
One consideration is that big temperature shifts can result in condensation. I suspect the powder dealers with unheated magazines turn over their stock frequently enough to ensure there is no time for temperature cycling to effect the quality of the powder, and that the majority of end users keep the powder at room temperature. If you have powder or for that matter ammunition on hand for years rather than weeks, where extreme temperature cycling takes place, it could effect the performance of the product.
Can I prove any of this? No. Will long term unheated storage result in misfires? I doubt it, but I do believe that temperature cycling over time has a detrimental effect. I recall when in my teens I found a box of .303 ammo with WW-1 date stamps left on top of the wall of my uncle's cabin out in the bush. Pulling one cartridge apart showed that it was charged with stick cordite. Upon firing the stuff it went bang, it was smokey and stunk, but I have no way of knowing if it functioned at full power. In those days I wasn't sophisticated enough to put up a target and compare the trajectory with my regular ammo. I was smart enough to know that the old stuff probably had corrosive priming and I gave my pride and joy a good scrubbing after all the ammo was shot up.
With respect to this business about temperature and performance of propellants, I recall reading a report from Africa, where a game department bought a large supply of factory .458 Winchester ammunition, and the stuff was used up slowly over a period of some years. Towards the end of the supply there were problems where one round would fail to penetrate and another would blow right through whatever beast it was directed at. A chronograph was secured and the rounds tested would drive the 500 gr bullets as slow as 1600 fps and as fast as 2300. The claim at the time was that the Winchester ball powder deteriorated from heat, but it could of just as easily been through frequent cycling between temperatures ranging from 50+C down to 0.
When I bring my rifles inside on a cold day, they immediately ice up, and so does the ammo and I suspect this occurs on internal surfaces as well. I've been trying to figure out how many cycles my ammo might see in the course of a winter, and I doubt if it's more than 100 because I swap the ammo out fairly frequently, but perhaps that might make for an interesting experiment next winter; let a few rounds cycle between -30 and +20 say 1000 times then chronograph them and see if the velocity is as consistent or significantly changed from those kept at a constant temperature.