The .22 stuff, no worry. The 12 gauge, could possibly be effected by the heat, but probably not. Before I retired, I worked in the central valley of CA, where 100+ temps are the norm in summer. We left Remington 870's, with four rounds of 00 buck in the mags, in the vehicles all the time. That is, 'til we discovered that the heat, combined with the tension of the mag spring, was causing the rounds to become deformed, or "bent" a little bit, right above the brass. Some to the extent that they would not chamber. Time for a policy change. But I doubt that loose rounds, or rounds in a box, would be adversly effected...
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OBG