MD80 FLT CREW RETURNED TO THEIR DEP ARPT WITH A #1 ENG FIRE WARNING.

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ENG FIRE INDICATION. THIS WAS THE THIRD LEG WITH THIS ACFT. THERE WAS A PREVIOUS WRITE-UP FOR A L FIRE LOOP B LIGHT ILLUMINATING WHICH HAD BEEN CLRED BY MAINT. THE FIRST LEG; ON CLBOUT FIRE LOOP B LIGHT ILLUMINATED; WE ACCOMPLISHED THE APPROPRIATE PROC CHKING THAT FIRE LOOP A WAS OPERABLE. CONTINUED TO LAS. AT LAS MAINT DEFERRED FIRE LOOP B. THE SECOND LEG; WITH OUTSIDE TEMP OF 86 DEGS (30 DEGS C) TKOF L ENG EGT AT 595 FOR 90 SECONDS. UPON LNDG SJC; MAINT INSPECTED AND CONFERRED WITH MAINT CTLR TECHNICIAN ALL WITHIN ENG LIMITS. ON THE THIRD LEG; AFTER TKOF; AT APPROX 4000 FT; FIRE LOOP A ILLUMINATED WITH A 'FIRE L ENG' WARNING. IMMEDIATELY REDUCED PWR; DECLARED EMER; TURNED BACK TO SJC; AND BRIEFED FLT ATTENDANT. WITH THE REDUCTION OF PWR THE FIRE WARNING AND LIGHTS EXTINGUISHED. REQUESTED ARFF/CFR AT SJC. LANDED OVERWEIGHT AT 137000 LBS; CLRED RWY 12L AND PARKED. REQUESTED AN EXTERIOR INSPECTION BY THE FIRE PERSONNEL AND TWR; THEN MADE A PA TO HAVE THE FLT ATTENDANT AND PAX TO REMAIN IN THEIR SEATS. THE L ENG AREA HAD NO INDICATION OF FIRE OR SMOKE AND I THEN TAXIED TO THE GATE. THERE WERE NO INJURIES OR DAMAGE. UPON DISCUSSION WITH THE MECHS I WAS SHOWN A STEEL ANTI-ICE DUCT THAT BROKE OFF THE L ENG SHOOTING HOT ENG AIR INTO ENG COMPARTMENT. SUPPLEMENTAL INFO FROM ACN 625842: WE LANDED WITH BOTH ENGS OPERATING DUE TO FIRE INDICATIONS DISAPPEARING AFTER THROTTLE ON AFFECTED ENG WAS RETARDED.