B757 Captain reported during cruise flight they experienced a right engine overheat EICAS resulting in aircraft operating with reduced performance. The crew continued to their destination airport.

Narrative

During the cruise portion of our flight at approximately 40 minutes into the flight at FL 380 we received a RT Eng Ovht on the EICAS and a RT Eng Ovht light on the center pedestal. The initial scan of the engine instruments did not show any signs of an overheat. We immediately looked at the Eng out page and confirmed the drift down speed and altitude. We opened our FM to 2.80.15 757 Rt Eng Ovht and proceeded to follow the procedure. Once we got to step 4 of the procedure and retarded the right engine throttle back slowly the RT Eng Ovht indications went out at approximately 60% N1. We then advised ATC that we had an Engine issue and we would need to descend to FL300. This was an altitude close to our engine out drift down altitude. We engaged the drift down speed and slowly descended to FL300. We did not initially [request priority handling] with ATC. We contacted our dispatcher and Maintenance Control and discussed our situation. At this point we were on step 8 of the procedure. We discussed all our parameters and options with the dispatcher and Maintenance Control and everyone agreed the situation was secured at this time and we were able to continue to the intended destination. The dispatcher ran a new fuel check and a new flight plan with the lower Altitude. During this discussion ATC gave us a new routing and a new ARRIVAL into ZZZ. This was discussed and the Dispatcher ran a new flight plan and advised us everything was the same. We all concluded that if the situation changed at all we would consider diverting into ZZZ1. But at this time that was not needed. After getting off the line with DISPATCHER and Maintenance Control we decided to [request priority handling] with ATC and no assistance was needed. We continued to run the rest of the procedure. After running Non-Normal Configuration Landing Distance tables in the Performance chapter (753 Green pages). I contacted our Dispatcher again to back me up on my calculation of the tab landing distance. The dispatcher came back to us with the same distance we had calculated. Once we were in contact with ZZZ approach we requested the longer Runway XXR. We requested Fire Department Assistance just in case the situation changed but advised we will taxi clear of the runway. Once we had a clear picture of our intentions I discussed our brief with the Flight Attendants. I also told the Flight Attendants to not alarm the passengers and not tell them we were an [priority handling] aircraft. During my top of descent brief I did tell the passengers we ran a small procedure and we will be met by the Fire Department trucks upon landing as a formality and to not worry or be concerned. We flew the ZZZ arrival to ILS XXR with partial flap procedures. We advised ATC that we were Thrust Deficient and in the event of a G/A that we would need to fly the Eng out special procedures. The approach was normal and we landed with no issues. The Fire department scanned our aircraft while we were taxiing to the gate and advised the engine scan was clean. We finished the taxi and shut down with no further issues. I debriefed the FO; a Customer Service Manager; two Maintenance Technicians and the Chief Pilot.