What was found
ON CLIMB OUT, RIGHT ENGINE OIL TEMP GAUGE WENT TO THE RED LINE AND HELD. AFTER A FEW MINUTES THE OIL TEMPERATURE WENT PAST THE RED LINE AND PRESSURE BEGAN TO DROP. PILOT SHUT DOWN THE ENGINE PER AMF PROCEDURES AND INFORMED CANCUN APPROACH, RIGHT ENGINE WAS SHUT DOWN DUE TO OIL TEMP AND REQUESTED RETURNING TO THE AIRPORT. THE PILOT WAS GIVEN VECTORS FOR THE ILS AND SAFELY LANDED. INSPECTED AND FOUND THE OIL WAS LEAKING FROM ENGINE NOSE CASE AREA, RETORQUED THE CASE BOLTS, NO HELP STILL LEAKING OIL FROM THE FLANGE. THE ENGINE WILL REQUIRE REPLACEMENT.