The pilot reported that he landed the Piper PA-28 at an airport near Pittsburg, Pa., and parked it to address an in-flight anomaly with his headset. He then performed a preflight inspection.
Before starting the engine, he pumped the primer twice and then attempted to start the engine. Subsequently, he observed smoke emanating from the engine area.
He continued attempting to start the engine while moving the mixture lever to the fuel “cutoff” position. He then observed flames emanating from under the engine cowling, discontinued attempting to start the engine, and exited the airplane.
Post-accident examination revealed extensive fire damage to the engine and airframe that appeared to have originated in or around the carburetor.
The Pilot’s Operating Handbook provided no guidance on using the primer when starting a hot engine, but stated that “engine fires during start are usually the result of overpriming.”
It is likely that the hot engine was overprimed, which resulted in excess fuel in the carburetor and the subsequent engine fire.
Probable cause: An engine fire, which resulted from the overpriming of a hot engine.
NTSB Identification: ERA15LA369
This September 2015 accident report is provided by the National Transportation Safety Board. Published as an educational tool, it is intended to help pilots learn from the misfortunes of others.

When in the USAF many moons ago…the instruction was while starting the big round engines that if a fire ensued to shut the fuel off, open the throttle and keep cranking and the fire would be sucked into the cylinders. Never had to try it but sounds good to me.
PA-28 engine fire:
If the engine was hot, there should ve no reason to have to prime it. A few pumps of the throttle to actuate the accelerator pump should be sufficient. From personal experience, for engines that prime the intake manifold upstream of the carb, it’s best to prime whike cranking the engine, no matter what the POH says. For example,the C-150 POH said to prime six times for a cold engine…..this soaks the induction box and nosewheel pant with gas, and a backfire may result in a “realfire”!