B767-300 First Officer reported a R ENG OVHT EICAS Caution Message and a R ENG OVHT Caution Light. The flight crew ran the check lists and QRH; retarding power on the engine until the light and ECAM extinguished. The flight crew continued to the destination airport; requesting priority handling and made a precautionary landing at destination airport.

Narrative

During climb passing approximately 16;000 feet we received an R ENG OVHT caution light and a R ENG OVHT EICAS (Engine Indicating and Crew Alerting System) caution message. The Captain (pilot flying) continued flying and assumed radio communication responsibilities while I (pilot monitoring) ran the QRH (Quick Reference Handbook). The QRH procedure called for disarming the auto throttle arm switch and reducing thrust slowly to determine if the OVHT light would extinguish. We requested a level off at FL250 while reducing thrust and the OVHT light and EICAS message went out at 79% N1. In accordance with the QRH we completed the appropriate branch of the R ENG OVHT QRH procedures and continued to ZZZ. After contacting ZZZ approach; we requested priority handling; landed on Runway XXC and stopped on the runway to allow ARFF to inspect the right engine and brakes. We opted to inspect the brakes due to increased landing speeds required by the QRH directed Flaps 20 VREF 20 landing configuration. No issues were noted by ARFF for the engine and brakes. The right engine was shutdown and taxi back to parking was uneventful.