Hot air?
I can well imagine different type engine controllers with a different type reponse to sudden changes in OAT. Anybody else know more?
Yes. Engine temperatures don't increase over the fire. Very little of aerial firefighting actually takes place in the heat or smoke column, and most retardant drops are done adjacent to the flame, or backing up dozer or hand lines, or natural barriers. Attacking the flame directly is done primarily with water, and even then it's drifting into the flame with wind, providing an aircraft some standoff from the fire itself. The times when one actually encounters increased heat over the fire arent' frequent, and when it happens, it doesn't affect engine performance.
The only thing I've ever seen affect engine performance over a fire is debris and smoke...which can flame out an engine, clog filters or screens, or contain debris on occasion that's large enough to block an air intake, carburetor, or otherwise do damage (breaking windscreens, etc).
The hollywood version of aerial firefighting that's seen in movies like "always" doesn't really do much to portray the real thing.