What was found
(CAN) CABIN DUCT HOT CAUTION LIGHT ILLUMINATED WHILE CLIMBING THROUGH 11,000 FT. CREW COULD NOT COOL DUCT IN AUTO OR MANUAL MODE, SO FOLLOWED QRH AND SELECTED PACK OFF. DUCT TEMP CAME DOWN GRADUALLY. ACM MAINTENANCE ACTIONS: RECIRC DIVERTER DUCT HOUSING REPLACED IAW AMM 21-25-06. GROUND RUNS CARRIED OUT AND ECS FUNCTION CHECK COMPLETED IAW AMM 21-60-01 WITH NO FAULTS FOUND IN AUTO OR MANUAL. TROUBLESHOOTING REVEALED A SHEERED SHAFT IN THE RECIRCULATION DIVERTER VALVE. RECIRCULATION DIVERTER VALVE REMOVED AS REQUIRED. RECIRCULATION DIVERTER DUCT HOUSING REPLACED IAW AMM 21-25-06. GROUND RUNS CARRIED OUT AND ECS SYSTEM FUNCTION CHECKED IAW AMM 21-60-01 WITH NO FAULTS FOUND IN AUTO OR MANUAL.