B737 Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 100; Flight Crew Total 975; Flight Crew Type 136
Aircraft Equipment Problem Less Severe
Air Traffic Control Provided Assistance; Flight Crew Landed As Precaution; Flight Crew Diverted
Aircraft
We were climbing from FL370 to FL390 and the #2 engine EGT (Exhaust Gas Temperature) rose into the amber. We descended back to FL350 and pulled the thrust levers back to diagnose the situation. I was PF (Pilot Flying) and the Captain was PM (Pilot Monitoring). We looked for an EGT Checklist (there isn't one) and eventually found and accomplished the Engine Surge checklist in the QRH. The EGT kept rising towards amber so we kept reducing power on the right engine. We ended up stabilizing at around .73 mach at FL350. There was enough of a throttle split that I was having to apply left rudder to keep the aircraft straight.We consulted [Maintenance] and Dispatch. [Maintenance] couldn't give us a definitive answer (or much information at all it seemed); however our Dispatcher was quite helpful with communicating. Any time we advanced the right thrust lever above around 79% N1; the EGT would start rising rapidly. We decided with dispatch that we had a degraded engine and were required by the [Manual] to divert to the nearest suitable field. We [advised ATC]; and diverted to ZZZ. The captain ran all the necessary checklists; we briefed the approach; and landed safely.In the descent the right engine indications normalized around 10;000 feet.Dispatch and Operations both did a great job.
B737 First Officer reported high EGT indication due to engine degradation.