B767-400 Captain reported a Left Engine Overheat message at FL310 and returned to departure airport.

Narrative

Just a few minutes after reaching our initial assigned cruise altitude of FL310; we had a L ENG OVHT EICAS (Engine Indicating and Crew Alerting System) message. I was the flying pilot and called for the QRC for said message. We ran the (767) ENG OVHT - L checklist as appropriate. Once I retarded the thrust lever as indicated in Step 4; the EICAS message extinguished. We continued through the checklist and maintained a thrust setting that maintained the ENG OVHT message not displayed as required. We were in clear skies and a non icing environment.At Step 9 of the checklist; I handed the controls over to FO (First Officer) in order to contact Dispatch and Maintenance Control. We sent them a brief message with the current failure and asked them to contact us via SELCAL. We called the back and had them wake up Relief Pilot who was on their rest break to come back to the FLT Deck. I also spoke with the Purser and advised them of our current engine overheat situation and that we would keep them appraised of the plan. Once on the line with Dispatch and Maintenance Control we collectively discussed the appropriate course of action. We also had them patch in our Chief Pilot for added consultation. As a crew; and after discussion with Dispatch; Maintenance Control; and our Chief Pilot; we determined that the safest course of action was to return to base and not continue across the Atlantic with a possibility of a more serious situation occurring should we continue.We contacted ATC and advised them of the need to return to ZZZ. We [requested priority handling] and due to the fact that we were going to land at max weight with Flaps 20 with a higher approach speed due to this non normal configuration.I again communicated with the Purser to advise her of our decision to return to ZZZ and an estimate of our time to landing. I made a passenger announcement advising them of our current situation and that in the best interest of safety we would be returning to ZZZ assuring them that we would be landing safely within an hour. As a crew; we made a plan and executed it. We had to dump our center tank fuel which was around 10K pounds to assist us in getting below our max landing weight. ATC authorized our fuel dump just north of the ZZZ1 area as we made our way towards ZZZ. We referenced the FOM for this procedure. Upon completion of the fuel dump we still needed to burn additional fuel so ATC gave us vectors on arrival. Again; we made another announcement to the passengers advising them of the personnel that would be following us to the gate in the interest of safety so that they would not be alarmed.We completed all checklists; continued to ZZZ without event; landed under our max landing weight; Flaps 20; with vehicles standing by for safety. After landing we taxied to gate. Our right side brakes entered the caution zone on the taxi in and we relayed this information to the crews for monitoring. After parking and with the aircraft chocked; and brakes not set; our brakes began to cool into the normal range.FO and Relief Pilot did an outstanding job using CRM as a crew throughout the course of this planning; communication; and execution of our return to ZZZ.