AT CRUISE ON BOARD MD80S; FLC SHUT DOWN ENG #2 DUE TO FIRE WARNING INDICATION. ACFT LANDED WITHOUT INCIDENT.

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I WENT TO THE COCKPIT TO INFORM CAPT OF AN ILL PAX AND TO FIND OUT HOW MUCH TIME WAS LEFT BEFORE WE LANDED. CAPT TOLD ME THERE WAS AN INDICATOR LIGHT INDICATING FIRE IN THE R ENG. THE CAPT AND FO CONTINUED TO PERFORM TESTS. THE CAPT KEPT US VERY INFORMED BY CALLING THE #1 FLT ATTENDANT INTO THE COCKPIT AT REGULAR INTERVALS. THERE WERE NO SECONDARY INDICATIONS OF THE FIRE. THE INDICATOR LIGHT; HOWEVER; WOULD NOT GO OUT. WE WERE TOLD THAT WE GOT DIRECT ROUTING TO DFW. THE CAPT FELT THAT THE INDICATOR LIGHT HAD MALFUNCTIONED; ALTHOUGH WE SOMEWHAT PREPARED FOR AN EMER EVAC; IN CASE WE GOT VISUAL INDICATION FROM THE TWR OF FIRE IN THE R ENG. THE R ENG WAS SHUT DOWN. THE CAPT INFORMED US NOT TO USE THE TAILCONE EXIT AND THE R WINDOW EXITS IN THE EVENT AN EVAC BECAME NECESSARY. WE BRIEFED THE PAX SEATED AT THE WINDOW EXITS AND GOT ASSISTANTS FOR THE DOORS WE WOLD BE USING. THE CAPT INFORMED THE PAX OF OUR SIT. THEY REMAINED CALM DURING THE REST OF THE FLT. WE DID NOT DO OUR PLANNED EMER CHKLIST AS PER CAPT'S INSTRUCTIONS. WE DID; HOWEVER; GET MENTALLY PREPARED. THE CAPT KEPT US VERY INFORMED OF THE SIT VIA THE #1 FLT ATTENDANT. ALTHOUGH I WAS A LITTLE FRIGHTENED; I FELT PREPARED TO COMPLETE AN EVAC IF IT WAS REQUIRED. WE LANDED WITHOUT INCIDENT AND PROCEEDED TO THE GATE.