B767-400 DIVERTS TO THE NEAREST SUITABLE ARPT AFTER INFLT SHUTDOWN DUE TO HIGH OIL TEMPERATURE.

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NORMAL TAXI; TKOF; CLB AND INITIAL CRUISE AT FL330. APPROX 25-30 MINS INTO THE FLT; RELIEF PLT LEFT COCKPIT TO START HIS CREW REST. WITHIN 5 MINS; FO BROUGHT TO MY ATTN A STATUS MESSAGE FOR THE L ENG CONTROLLER. AFTER A BRIEF DISCUSSION; WE CONTINUED. AFTER ANOTHER 3-5 MINS; I NOTICED THE OIL PRESSURE ON THE L ENG FLUCTUATING BTWN 10-21 PSI (IN THE AMBER BAND); LOOKED AT THE OIL QUANTITY AND SAW THAT IT WAS INDICATING ZERO AND BROUGHT THIS TO THE FO'S ATTN. AT THIS TIME WE WERE APPROX 60 MI S OF ZZZ; DECIDED TO START A TURN BACK TO ZZZ1 WITH THE FO COORDINATING WITH ATC AND I CALLED FLT ATTENDANTS TO HAVE THE RELIEF PLT COME TO THE COCKPIT. ONCE THE RELIEF PLT RETURNED TO THE COCKPIT; WE HAD BEEN CLRED DIRECT TO VOR TO RETURN TO ZZZ1. I XFERRED CTLS TO THE FO SO I COULD CONTACT OPS CTL VIA SATCOM AND ASKED THE RELIEF PLT TO RUN THE ENG OIL PRESSURE CHKLIST. DURING MY CALL TO OPS CTL; I WAS PATCHED INTO MAINT CTL AND DESCRIBED OUR SITUATION. WHILE DISCUSSING OUR OPTIONS WITH OPS CTL; THE OIL TEMP REACHED REDLINE AND THE RELIEF PLT AND FO RAN THE OIL TEMP CHKLIST AND SECURED THE L ENG AND I INFORMED OPS CTL OF THE ENG BEING SECURED AND THE DECISION OF DIVERTING TO ZZZ WITH AN ARR TIME IN APPROX 15 MINS AND DECLARED AN EMER WITH ATC AND RECEIVED A CLRNC TO PROCEED DIRECT TO THE OM FOR THE ILS XX AT ZZZ AND STARTED A DSCNT. THE RELIEF PLT PULLED THE APCH CHARTS FOR ZZZ AND I COORD WITH THE FLT ATTENDANTS AND MADE A PA TO BRIEF THE PAX ON THE SITUATION. AT APPROX FL200 I RETURNED TO THE CTLS AND WAS BROUGHT UP TO SPD ON WHAT HAD BEEN COMPLETED AND THAT WE WERE CLRED DIRECT TO THE OM AND TO 3000 FT. THE FO AND RELIEF PLT CONTINUED ON THE 1 ENG INOP APCH AND LNDG CHKLIST AND WERE VECTORED ONTO THE ILS. BTWN 3000-4000 FT; I DISCONNECTED THE AUTOPLT TO GET A FEEL OF HOW THE ACFT WAS HANDLING AND COMPLETED AN OVERWT LNDG (30000 LBS OVER MAX GROSS LNDG WT) WITH MINIMUM DSCNT RATE AT TOUCHDOWN DECELERATED TO TAXI SPD WITH BTWN 2000-3000 FT REMAINING; TAXIED TO THE END; CLRED THE RWY AND SECURED THE R ENG AFTER THE AFTER LNDG CHKLIST. AT THE END WE WERE INSPECTED BY CFR PERSONNEL WHO RPTED NO DAMAGE TO THE L ENG AND THE BRAKES WERE NOT OVERHEATING. WE REQUESTED A TUG AND WERE TUGGED TO THE GATE WITHOUT INCIDENT. COMPLETED PARKING CHKLIST AND MADE LOGBOOK ENTRIES.