Ammunition doesn't seem to degrade too badly in the Middle East.
That is because the military uses mil-spec powders designed to not be as temperature sensitive. Most powders will see a velocity change of about 1 fps for each degree of temperature change. Most loads are developed at around 70 degrees.
Ammo that is fired when it is 170 degrees, which is not out of the question for ammo inside a vehicle in hot climates, could easily be 100 fps faster than designed, and be overpressure. At -30 it could be 100 fps slower, and make sight adjustments incorrect.
There are some powders which would only see 20-25 fps velocity change at the same temperatures extremes. Those are the ones used by the military. The ones I prefer to use as well.
I don't see any possible damage to a gun. Some steel guns might be too hot to hold. It is possible the ammo could be degraded over time, or even dangerous if fired while it is hot.