What was found
DURING CLIMBOUT THROUGH 4000 FT, THE RIGHT ENGINE FIRE WARNING SOUNDED. WITH THE POWER REDUCED, THE LOOP AND FIRE HANDLE LIGHTS WENT OUT. NO FURTHER FIRE INDICATIONS WERE NOTED. FLIGHT CREW DECLARED A YELLOW EMERGENCY, RETURNED TO BTR, AND LANDED WITHOUT INCIDENT. OVERWEIGHT LANDING WAS MADE AT 83,200 LBS. MAINTENANCE REPLACED A BROKEN NOW COWL ANTI-ICE DUCT, RIGHT ENGINE AND ACCOMPLISHED OVERWEIGHT LANDING INSPECTION. OPERATIONAL CHECK NORMAL.