I've been "pinged" countless times by ammunition cooking off in house fires in my 30+ years of firefighting. The bullet basically lays there as the case splits open. As Steve so aptly points out, the case slits open and dumps the pressure out harmlessly to the air. The primer is often pushed out at a high velocity but it is so light that it acts like a ping pong ball and quickly slows down. At near contact distance the primer will not penetrate turnout gear nor damage the face piece of our breathing apparatus.
In most cases we will not even realize ammo is igniting as there are so many other objects and substances making much the same noises. The risk from uncontained ammo is so low that I can only recall a couple of articles regarding this in my career. Hairspray and other aerosols are mentioned much more often to give an idea which the fire service considers more hazardous.
The most recent mentions of ammo igniting in a fire actually involved loaded guns. The ammo in the chamber did act much as if normally fired but the rounds in the magazine just split and fizzled.
There was one case where a semiauto did fire multiple times but it was thought a very rare circumstance as it would be difficult to heat a barrel/chamber enough to ignite the chambered round but not enough to cause the ammo in the magazine to not cook off. I seem to recall mention of heat inpingement on the barrel with the rest of the action shielded in some way. It seemed odd to me but it is the only way I can see for multiple shots to be fired.
SAAMI has a rather interesting video of how ammunition responds in a fire, it is a bit better than the one done be Federal Cartridge and the Fridley, MN Fire Department in the late 70s or early 80s.
Ammo laying in the open is not a problem when exposed to heat. It could be if contained in a vessel such as a chamber.
