SF340 FLT CREW REPORTS ENGINE INLET ANTI-ICE FAILURE CAUSING BURNING SMELLS. FLT CREW COMPLIES WITH QRH; DECLARES AN EMER AND RETURNS TO DEPARTURE ARPT.

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CLBOUT WAS ROUTINE WITH MULTIPLE STEPS (4000 FT; 5000 FT; 7000 FT). AFTER REACHING 7000 FT; WE WERE ASSIGNED TO CLB AND MAINTAIN 11000 FT. SHORTLY AFTER INITIATING THE CLB FROM 7000 FT; WE RECEIVED A R-HAND ENG INTAKE LIGHT. ALONG WITH THE INTAKE CAUTION LIGHT; THE FO AND I BOTH SMELLED A VERY STRONG ODOR OR BURNING -- MELTING RUBBER. I ASKED THE FO TO CHK THE CONDITION OF THE R ENG INTAKE AREA. HE RPTED SEEING LIGHT COMING FROM WITHIN THE INTAKE AREA; WHICH I THOUGHT TO BE FIRE. I IMMEDIATELY TURNED THE R-HAND ENG HEAT SWITCH OFF AND THE FO RPTED THE LIGHT FROM INSIDE THE INTAKE EXTINGUISHED. WE THEN ASKED DEP FOR RADAR VECTORS BACK TO ZZZ AND RPTED TO THEM WE HAD AN ENG ANTI-ICE PROB. THE FO READ THE QRH CONCERNING THE ILLUMINATED CAUTION LIGHT. AT THIS POINT; THE FO TOOK OVER FLYING DUTIES SO THAT I COULD TAKE OVER THE COMS. AFTER A FEW MOMENTS TO THINK THROUGH THE SITUATION; I CALLED DEP AND DECLARED AN EMER; STATING THE NATURE OF THE PROB (FIRE ON THE R ENG INTAKE) AS WELL AS RPTING THAT THE FIRE HAD EXTINGUISHED BY TURNING THE ENG ANTI-ICE OFF. DEP ACKNOWLEDGED AND STATED THAT EMER VEHICLES WOULD BE STANDING BY. WE WERE THEN GIVEN VECTORS TO THE FINAL APCH COURSE. AT THIS POINT; I CALLED DISPATCH AND NOTIFIED THEM OF THE SITUATION; RPTED TO THE FLT ATTENDANT; AND MADE AN ANNOUNCEMENT TO THE PAX STATING THAT WE WOULD BE RETURNING TO ZZZ. WE DECIDED THAT SINCE THE FO WAS CURRENTLY FLYING AND COMFORTABLE THAT HE WOULD MAKE THE APCH AND LNDG INTO ZZZ. WE ACCOMPLISHED THE DSCNT AND APCH CHK AND FROM THERE A NORMAL LNDG. WE TAXIED OFF THE RWY AND STOPPED LONG ENOUGH TO ASSESS OUR SITUATION. WE THEN COMMUNICATED TO GND CTL THAT THERE WAS NO FURTHER NEED OF ASSISTANCE. WE THEN TAXIED BACK TO THE GATE. THE POSTFLT INSPECTION FOUND A BURNT SPOT ON THE R-HAND ENG INTAKE. THE EVENT WAS FIRST IDENTED BY A MASTER CAUTION; ICE PROTECT LOOKUP LIGHT; AND R INTAKE LIGHT. ALONG WITH THE CAUTION LIGHTS; BOTH THE FO AND I SMELLED A STRONG ODOR OF BURNING/MELTING RUBBER. THE FO THEN SAW A LIGHT COMING FROM INSIDE THE R-HAND ENG INTAKE.