AN ACR FLC HAS A FIRE WARNING INDICATION ON THE R ENG AND DOES A PRECAUTIONARY SHUTDOWN WHEN THEY ARE UNABLE TO CONFIRM AN ACTUAL FIRE EXISTS.

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DSNDING FOR APCH IN SYR; THE R FIRE HANDLE ILLUMINATES. I COMMAND THE FO TO EXECUTE THE INFLT ENG FIRE CHKLIST. WE DETERMINE THAT THERE IS NO FIRE AND ADVISE ATC THAT WE HAVE MADE A PRECAUTIONARY ENG SHUTDOWN. THEY ADVISED THAT THE VOR RWY 32 WOULD BE MOST EXPEDITIOUS AND THE WINDS WERE 310 DEGS AT 17 KTS FAVORING THAT RWY. I ELECTED TO ACCEPT THE VOR RWY 32 APCH BASED ON THIS INFO AND REQUESTED THE EMER EQUIP STAND BY AS A PRECAUTION. THE FO THEN ADVISED OUR PAX. NEXT THE FO BRIEFED THE APCH. I CALLED FOR THE ONE ENG INOP CHKLIST. ALL ITEMS WERE ACCOMPLISHED. ATC SWITCHED US TO THE TWR FREQ; TWR ADVISED US THAT THE EQUIP WOULD BE IN PLACE AND CLRED US TO LAND. THE LNDG WAS UNEVENTFUL. UPON CLRING THE RWY WE ACCOMPLISHED ALL AFTER LNDG CHKS AND TAXIED TO THE GATE. PARKED AT THE GATE; WE DETERMINED OUR PAX TO BE UNHARMED AND IN NO WAY ADVERSELY EFFECTED. OUR MAINT DEPT WAS NOTIFIED. UPON INSPECTION OF THE ENG; THEY DETERMINED THAT THE FIRE LOOP SENSING EQUIP HAD MALFUNCTIONED CAUSING THE FIRE HANDLE TO ILLUMINATE.