Just a thought, but fire depends on having heat, fuel, and oxygen in close proximity..... A dive, while providing more O2, would tend to remove heat from the reaction, and the increased speed would tend to drag the point of combustion away from the fuel source untill the fuel was too diluted to maintain combustion. Dont really know, but that is my best guess.
Oxygen is everything when it comes to burning. Burning is in other terms a very rapid spontaneous process of oxidization which emits heat.
If a plane dives very fast, an isolated source of fire may temporarily run out of oxygen because the airflow could become so fast that the rate oxygen is burned out is faster than it is resupplied. So in some cases, it is possible to expect fires to die out.
However, as the vast majority of cases of onboard fires are caused by ignition of the fuel, the moment the plane slows down from a dive it is very likely the fires will start again.
Another source of common fires, is the hydraulic fluids burning out. This is very commonly seen in guncams, where an explosive cannon shell lands on certain sections of the plane - typically near the wing roots - and setting ablaze the hydraulics related with landing gears. These start a small, local fire at the wings, and then subsides and dies out as the hydraulic fluids are all spent.
Another simular incidence is when wing tanks with very little fuel left, catch fire and burn away, but not large enough to consume the whole plane, and eventually dies out.
IL2/FB depicts these fires - it's really cool to watch. You can see them most commonly on P-38s and Ki-84s.. the plane bursts into flames near the wings, and then after a while the flame dies out.
