The pilot reported that he intended to go on a local area personal flight. He performed the preflight inspection in the hangar. He pulled the airplane out of the hangar, started the engine, and taxied to the runup area for runway 16. When he reached the runup area, he shut the engine down and retrieved two headsets from the airplane's baggage compartment. He returned to the cockpit and started the engine. He did not prime the engine because it had recently been running. The engine restarted with no apparent problems. As he turned to retrieve the pretakeoff checklist he felt heat on his face. He looked but did not see the source; however, the heat increased. As he looked out of the door he saw flames emanating from under the front of the engine cowling. Then, he pulled the mixture control to the lean position to shut down the engine and evacuate the airplane. The Federal Aviation Administration accident coordinator examined the airplane. Fire damage was evident in the aft engine area, and the cockpit area was consumed. Examination of the gascolator showed that the fuel line fitting at the gascolator that connected the line to the fuel pump leaked. Based on a review of the logbooks, the accident coordinator stated that no recent maintenance had been performed on the fitting.