What was found
ON CLIMB-OUT THE NR 2 ENGINE OIL TEMPERATURE WENT INTO THE RED ARC (216 DEGREES) AND STAYED THERE. EVEN AFTER THE ENGINE WAS REDUCED TO IDLE THE OIL TEMPERATURE REMAINED IN THE RED ARC, SO PER THE QRH THE ENGINE WAS SHUTDOWN. THE CREW RETURNED THE AIRCRAFT TO CUN AND AN UNEVENTFUL LANDING. CORRECTIVE ACTION: MAINTENANCE FOUND EXCESSIVE OIL IN THE GEARBOX. THE MAIN GEARBOX SCAVENGE PUMP AND LSOP WERE REPLACED. HIGH OIL TEMPERATURE INSPECTIONS WERE PERFORMED WITH NO FINDINGS. PRATT AND WHITNEY CONTACTED FOR 1 TIME FERRY FLIGHT TO ATL. FERRY FLIGHT PERFORMED AND THE ENGINE WAS REPLACED UPON ARRIVAL.