The first thing you do when a fire breaks out is to turn off the transponders and turn west and fly for 4 hours.
IIRC, a pilot was interviewed who claimed that there was a fire on the plane, at which point the pilot did his best at maneuvering to deprive it of oxygen, then made a left hand turn toward the nearest airport. He speculated that smoke overwhelmed the interior and the plane was then on autopilot, when it flew for four hours and then into the ocean. This theory does sound plausible to me, but it may or may not be correct.