What was found
PILOT REPORTED #1 ENGINE FIRE WARNING LIGHT DURING FLIGHT. THIS LIGHT INITIALLY BEGAN TO FLICKER, THEN WENT ON SOLID WITH AURAL TONE. THE PILOT CHECKED ALL ENGINE INSTRUMENTATION, AND THEY ALL WERE ALL IN NORMAL RANGE. HE THEN PERFORMED A VISUAL WITH THE ASSISTANCE OF THE CREW WITH NO VISUAL INDICATION OF A FIRE. AT THIS TIME, THE LIGHT BEGAN TO FLICKER AGAIN, AND THEN WENT OUT. THE PILOT THEN REDUCED POWER, AND CHOSE TO CONTINUE FLIGHT TO THE PLANNED AIRPORT DESTINATION. AFTER ABOUT ONE MINUTE, A BRIEF BURNING SMELL WAS FOLLOWED BY THE #1 ENGINE FIRE LIGHT AND AURAL TONE AGAIN. AT THIS TIME, THE PILOT ESTABLISHED OEI/EMERGENCY PROCEDURES. THE FIRE BUTTON WAS DEPRESSED (BOTTLE DISCHARGED) AFTER THE N1 DROPPED BELOW 50%. AFTER ONE MINUTE, AND THE #1 ENGINE FIRE LIGHT STILL ILLUMINATED, THE #2 FIRE BOTTLE WAS DISCHARGED AS WELL. AN UNEVENTFUL SINGLE ENGINE RUN ON LANDING WAS PERFORMED WITH NO EVIDENCE OF FIRE FOUND BY EITHER THE PILOT OR MYSELF FOLLOWING SHUTDOWN OF THE REMAINING ENGINE. TROUBLESHOOTING DETERMINED THAT THE #1 ENGINE AFT OUTBOARD FIRE PROBE TO BE CLOSING BEFORE THE CORRECT TEMPERATURE (PROBE ORDERED). AS FOR THE BRIEF BURNING SMELL THAT OCCURRED DURING THE SECOND LIGHT EVENT, THE SOURCE COULD NOT BE IDENTIFIED. THIS AIRCRAFT REMAINS OUT OF SERVICE AT THE TIME OF THIS SUBMISSION AWAITING THE FIRE DETECTORS AND REPLACEMENT FIRE BOTTLES.