Captain flying 777 aircraft reported EGT exceedance during takeoff climb. Flight crew returned and landed uneventfully.

Narrative

The flight departed ZZZ Runway XXL on the ZZZZZ RNAV Departure to 3000 feet. At approximately 1500 feet the Captain noted to the crew; potentially conflicting aircraft traffic at approximately the 2 o'clock position. At about the same time; one of the Relief Pilots called out an overtemperature exceedance on the right engine. The Relief Pilot also noted that the right engine EPR had initially started to drop. The Captain then turned the autopilot on and slowly retarded the right engine throttle attempting to get the right engine EGT back below the temperature exceedance. At approximately the idle position the temperature remained below the temperature exceedance and back into the normal temperature operating range but at what appeared to be an elevated temperature for the idle position. At this point; the Captain elected to intercept the ZZZ XXX radial outbound per the engine failure procedure for Runway XXL even though the aircraft was at 1500 feet since the aircraft was climbing out very slowly and the Captain wanted to ensure terrain clearance while continuing to climb to 3000 and run checklists. The First Officer [requested priority handling] for the flight and told ATC the flight would be initially intercepting and proceeding outbound the ZZZ XXX radial while working the [situation].There were no EICAS messages or automatic Non-Normal Checklists displayed on the EICAS so the crew elected to perform the Engine Lim/Surge/Stall checklist on the right engine. As the First Officer performed the checklist; it was noted that the right engine temperature would increase abnormally higher as the right engine throttle was increased out of idle. As a result of the checklist; the crew decided to bring the throttle back to idle. The crew discussed the options for the right engine and decided to keep the right engine running in idle for the remainder of the flight unless absolutely needed. The crew reasoned this to be the most prudent action since the engine was still producing thrust; was at a stable but elevated temperature at idle (than normally expected) but still in the normal temperature operating range; was not operating erratically and did not appear to be damaged. Once the aircraft was stable and the Non-Normal Checklist was complete; the Captain directed the First Officer to request vectors from ATC to an area near the ZZZ airport that we could safely jettison fuel. While getting these vectors the Captain gave control of the aircraft to the First Officer so that the Captain could coordinate with dispatch; Maintenance Control and the flight attendant. The Captain asked the Relief Pilot to call the flight attendant and inform them of the current aircraft situation and that we would most likely be returning to ZZZ. Also; the Relief Pilot was instructed to make a PA announcement updating the passengers. In the meantime; the Captain was able to coordinate a discussion with dispatch and maintenance control. Maintenance Control noted that from his equipment sensors and readings of our aircraft that the exceedance was real and not a spurious indication. The crew discussed and was in agreement that the flight should return to ZZZ after jettisoning fuel. The Captain informed dispatch and Maintenance Control of the crew's decision to return to ZZZ and asked for any other recommendations for the engine issue; jettisoning fuel and coordination for the return to ZZZ. Maintenance Control gave no further guidance and noted the crew's intention to return to ZZZ and stated he would coordinate with Maintenance. Dispatch reminded the crew to annotate the time; location and fuel amount at the beginning and end of the fuel jettison process. Dispatch also indicated that he would calculate landing data for the return to ZZZ. Once the crew arrived at the ATC coordinated fuel jettison area the Captain initiated the Fuel Jettison checklist. The crew decided to jettison fuel down to the max landing weight so that the overweight checklist would not have to be run and a maintenance overweight inspection would not be required. The fuel jettison procedures for the amount of fuel onboard took approximately 30 minutes. During this time period the crew monitored the right engine for any changes and discussed and prepared the flightdeck for the descent; approach; landing; Airport Rescue and Fire Fighting (ARFF) coordination and return to the Gate. The crew anticipated a normal landing and decided that if there were no issue upon landing that they would coordinate to clear the runway and have ARFF inspect the right engine on the Taxiway for any issues prior to taxiing to the gate. Upon completion of the Fuel jettison checklist; the Captain briefed the crew for a single engine flaps 20 ILS approach to Runway XXR. Dispatch was having difficulties with the landing data so the Relief Pilot ran the landing data numbers for a single engine landing. The checklists were completed for descent/landing and the Captain flew the single engine approach to Runway XXR for an uneventful landing. Upon landing the Captain cleared the Runway and ARFF inspected the right engine; found no issues; so the flight continued to Gate. The passengers were then deboarded to the gate area and turned over to the gate agents. At the gate the crew debriefed maintenance concerning the right engine temperature exceedance. The crew noted to maintenance that the exceedance temperature was approximately 666 degrees celsius. Also; from the point the crew noticed the exceedance to the point the Captain promptly retarded the throttle to idle; the time duration was approximately one minute. The Captain then debriefed with the flight attendants and with the gate agents. The Captain and the flight crew then debriefed with Dispatch and the Chief Pilot through a telephone conference call. Finally; the flight crew debriefed their own performance.