What was found
AOA HEAT FAIL ILLUMINATED IN FLIGHT. AFTER A SHORT TIME, THIS LIGHT EXTINGUISHED. SEVERAL MINUTES LATER THE RT ENGINE FIRE DETECT SYSTEM AMBER ANNUNCIATION AND MASTER CAUTION ILLUMINATED. DURING THE TIME IT TOOK TO PULL OUT THE CHECKLIST FOR THIS LIGHT IT EXTINGUISHED, AND THEN THE RT ENGINE FIRE RED SWITCH LIGHT ILLUMINATED. THE RT THRUST LEVER WAS PULLED BACK TO IDLE IAW THE MEMORY ITEMS FOR AN ENGINE FIRE INDICATION. THE FIRE INDICATION EXTINGUISHED WITHIN 15 SECONDS OF PULLING THIS THROTTLE TO IDLE. AT NO POINT DURING THIS OCCURRENCE WAS THERE ANY SECONDARY INDICATION OF AN ENGINE FIRE.