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So... ammo in a gun is bad if heated up... but ammo in a box is not going to explode upon heating?
Don't know - we always considered munitions as a hazard during a fire. Then again, we were dealing with 20 and 30 millimeter ammunition - not exactly deerhunting rounds.
The gunpowder will still ignite, but the moment the slug leaves the jacket, all of the energy is released and little of it propels the bullet. If the round is in a gun, it is propelled with the full force of the chemical expansion, and all in one specific direction down the length of the barrel.
Compare the water calmly burbling out of your garden hose before and after you stick your thumb on the opening, either dispersing the force over a large area (the opening of the hose) or channelling it all in one direction.
Rounds in barrels in a fire will cook-off, where the pressure will build up due to the containment of the chamber and rifling retarding the bullet travel. The round will fire at full velocity. Fortunately, many powerful long guns are stored muzzle up in racks or safes, and pistol rounds are significantly less energetic.
If the round is chambered it has the potential to become a projectile. Rounds in a guns magazine will not become projectiles if over-heated.