While the oven is preheating, allow me to postulate that the thermal mass of the barrel, especially in vicinity of the breech, would require far more exposure to heat to reach the temperature required for the powder to spontaneously ignite.

This is why hot gun cook-offs occur, because the barrel has absorbed enough heat that it's able to ignite the powder through the casing via conduction. As such, as you would expect, after containing a single explosion (i.e. firing a round), the chamber would be warm to the touch while the exterior of the barrel would remain cool. It's not until the metal is exposed to enough heat internally that the barrel becomes too hot to touch externally.

So that's my logic here. If it was suddenly 500 degrees outside, I think the safest place to hide a bullet in a gun to keep it from exploding is the chamber.