What was found
AS THE AIRCRAFT CLIMBED THROUGH 4000 FEET, THE FLIGHT ATTENDANTS INFORMED THE COCKPIT CREW THAT THE AFT RIGHT LAVATORY SMOKE DETECTOR WAS SOUNDING AND THAT THE CABIN HAD A HOT SMELL. FLIGHT CREW MADE NOTE OF POWER SETTINGS AND RETURNED TO A NORMAL SAFE LANDING BACK AT MSP. NO MENTION OF COMPLIANCE OR CABIN HEAT SELECTOR POSITION. MAINTENANCE PERFORMED "SMOKE IN CABIN" TROUBLESHOOTING PROCEDURES AND FOUND A CRACKED DUCT BETWEEN THE LEFT ACM AND COALESCER BUT NO SOURCE OF SMOKE. AFTER THE DUCT WAS REPLACED AND THE COALESCER BAGS CHANGED, PACK BURN OUT PROCEDURES WERE COMPLIED WITH. THE AIRCRAFT HAS RETURNED TO SERVICE.