FLC EXPERIENCED ENG FIRE. INFLT ENG SHUT DOWN AND DECLARED EMER AND LNDG.

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ENRTE WE HAD USED THE ENG ANTI-ICE SYS DUE TO ICING CONDITIONS (PLUS 5 DEGS CENTIGRADE AND VISIBLE MOISTURE). AFTER A FEW MIN OP THE WARNING LIGHT ILLUMINATED BRIEFLY AND BEGAN TO CYCLE ON AND OFF EVERY 2 OR 3 MIN. WE NOTED AN ODOR OF BURNING RUBBER BUT THAT WENT AWAY. WE RAN OUR EMER PROC FOR AN INTAKE LIGHT (R SIDE). THE CHKLIST INDICATED THE SYS WAS LIKELY TO BE CYCLING UP AGAINST AN OVERTEMP CTLR. ITS ONLY DIRECTIVE WAS TO LEAVE ICING CONDITIONS AS SOON AS POSSIBLE. WE LEFT ICING AND SHUT OFF THE SYS. ON BEGINNING THE DSCNT WE RE-ENTERED ICING CONDITIONS AND TURNED THE SYS BACK ON. AGAIN THERE WAS A BRIEF ODOR. THE SYS ONCE AGAIN STARTED CYCLING; AND WE WERE TOLD TO CONTACT APCH. THE CTLR GAVE US A HDG TO JOIN THE LOC AND CLRED US DOWN AND SUBSEQUENTLY CLRED US FOR THE APCH. WHEN I GLANCED AT THE FO I NOTICED SOME REDDISH YELLOW FLASHES OUT HIS WINDOW. I HAD HIM VISUALLY CHK THE R ENG. HE INDICATED THERE WAS A FIRE OF SOME TYPE AND WANTED TO DO THE EMER CHKLIST FOR AN ENG FIRE WHICH CULMINATES IN AN ENG SHUT DOWN. WE EXECUTED THE PROCS AND SHOT A NORMAL SE APCH AND LNDG. NO INJURIES OCCURRED AND THE ACFT SUSTAINED ONLY DAMAGE TO A DEICE BOOT ON THE R SIDE OF THE FORWARD PORTION OF THE R INTAKE.