Nothing to worry about unless you're lugging around old waxed paper shotshells...

Smokeless powder does not love long term elevated temperatures, but essentially all that does is deteriorate the powder faster (less velocity). If you are REALLY worried about it, change the ammo annually by shooting up what was stored in your vehicle and replacing with either new ammo or ammo that has ben stored in more moderate temperatures.

There are some conditions that can cause pressures to shoot way up; the classic" scenario is a hot reload for a large caliber rifle is developed in cool weather in the states, then taken to a tropical country for hunting. A load that was to-the-wall max in an already high pressure cartridge can go "over the line" for safe pressures in tropical heat. <shrug> That's not your case; don't worry about it. (and it's not as common a problem as some think, anyway)

Cold weather? Don't worry about it. It will fire fine with no harm to the weapon. However, there are things to remember about bringing a cold piece of metal into a warm house - moisture will condense on it like on a cold beverage glass in July. Best to keep it in a sealed moisture-proof bag (ziplock) until it is at room temperature if you bring it in from the cold. The other consideration for extreme cold is that some lubricants will become so stiff - even just a light film - that the weapon may not cycle properly, making it a single shot. Again, that's not a common problem in temperate climates, but if you regularly get arctic winter temps, it may be. There are two solutions: No lube (fairly simple solution) or fancy lubes designed for those extreme low temps.