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In this context, heat and pressure are locked together. Increase in pressure = increase in temps. As volume expands, pressure goes down and so does temperature. Gas temps inside the casing at ignition are about 5000F for a microsecond - and as soon as the bullet moves forward, temps start dropping rapidly. It's about 4000F an inch or so past the chamber, and about 1500-2000F by the time the bullet exits the muzzle, depending on cartridge and barrel length.