What was found
THE CREW REPORTED THAT AFTER TAKEOFF & CLIMBING OUT THROUGH 2000 FT MSL THE LT ENG FIRE WARNING SYS ACTIVATED. THE LT ENG WAS BROUGHT BACK TO IDLE IAW THE CHECKLIST & AFTER 3 - 4 SECONDS THE FIRE WARNING EXTINGUISHED. THE CREW COMPLETED THE CHECKLIST ITEMS & REQUESTED TO RETURN BACK TO THE AIRPORT FOR LANDING & REPAIRS. THE RETURN FOR LANDING WAS UNEVENTFUL. INVESTIGATED FOR DAMAGE BUT NONE WAS NOTED, NO BLEED AIR LEAKS WERE NOTED. FURTHER INVESTIGATION FOUND THE FIRE LOOP DETECTOR ON THE INBD SIDE OF THE LT ENG WAS RESTING ON THE BLEED AIR CONNECTION COMING OFF ENG. THE FIRE DETECTOR WAS REPOSITIONED IAW THE AMM & FUNCTIONAL CHECKS WERE SATISFACTORY. THE ACFT WAS RETURNED TO SERVICE.