The activation temperature of gunpowder is around 400 - 450 degrees F. If you’re pre-heating the oven for a turkey you should be fine. Self-cleaning the oven the you’ll soon need to do some remodeling of your kitchen.
I watched some video (after watching a movie with the fire setting off the ammo and the bullets “shooting” all over the place) about what really happens with ammo during a fire.
It just does a lot of popping but no velocity. It was some fire department doing training. Then another one was a demonstration. The wooden building mock-up contained the small explosions as the rounds popped off.
But yes - the kitchen would probably need some work done on it. The small explosions would probably be enough to blow the door open.
It varies according to powder (single base, double base, and other factors) but Hodgdon's SMS sheets for both Benchmark and Varget list temperature of spontaneous ignition at 338°F. I think most if not all will ignite before 400°F. The higher the temperature of spontaneous ignition is, the harder it is for the primer to set it off.
And that's a separate matter from spontaneous ignition of the primer, because if the primer "cooks off," the cartridge will go BANG! just as surely as if you'd pulled the trigger on it.
I've never found a source I was happy with about spontaneous ignition temperature for primers but the Wikipedia page for lead styphnate (the primary explosive used in most modern firearm primers) says it autoignites at 626°F. But primer compound also contains several other chemicals (lead dioxide, barium nitrate, tetrazene, et Al), which doubtless changes that temperature.
Oven?
Italian Explosives Expert: The Beirut Blast’s Massive Red Cloud is Indicative of Lithium Metal Which is a Propellant in Military Missiles — IT WAS AN EXPLOSIVES STORAGE FACILITY
https://www.thegatewaypundit.com/2020/08/italian-explosives-expert-beirut-blasts-massive-red-cloud-indicative-lithium-metal-propellant-military-missiles-explosives-storage-facility/
(I have link to one surviving video with a working URL and it shows double blasts, first with boom, 2nd with whirling effect followed by huge BANG. What deflected the blast? The silo partial, the whirling pre 2nd Blast deflected the blast upward.)
THE “SELF-CLEANING” FEATURE ON OVENS===RAISING THE INTERNAL TEMP WAAAAAY UP...
TURNING EVERYTHING INTO ASHES.
ALSO COSTS YOU A SMALL FORTUNE IN ELECTRICITY BILLS.
NOT SURE THOSE FEATURES RE STILL OFFERE