An air carrier First Officer reported an engine overheat warning during cruise which resulted in a diversion to a nearby airport.

Narrative

In cruise we suddenly got an EICAS warning L ENG OVHT. I was pilot flying and CA pulled the non-normal checklist. Part of the checklist involves retarding the throttle on the affected engine to see if the warning goes away. Just slightly above flight idle; the warning went out. CA continued through the rest of the checklist. Due to the fact that we were operating on a single bleed he attempted to start the APU. We then got an APU FAULT EICAS message and a APU low oil status message. The CA then tried to use the SATCOM to contact dispatch and maintenance control to discuss the situation. This is when we discovered that the SATCOM system was also not working. We then did a 'CALL ME' to dispatch and got a VHF frequency. After the CA described the situation to maintenance control and dispatch; it was determined that the best course of action was to request priority handling and divert to ZZZ. CA informed the Purser of the situation and relayed to the FAs that we would be landing fast as well as overweight so possibility of a brake fire existed but because we were landing on a long runway; we should be ok; but to expect to see emergency vehicles around the plane upon landing. CA also made a PA to the passengers. We received an amended clearance from ATC and set up for a visual approach backed up with the ILS with vectors to final. I performed the landing and utilized thrust reverse on the good engine and auto brakes to slow down. We exited the runway and had ARFF (Airport Rescue and Firefighting) inspect the aircraft for damage and/or fire. Brake temps were either 4 or 5 for all wheels; but never went higher. We had informed operations of our inoperative APU status and as we pulled into the gate; left only 1 engine running till ground power was connected. We subsequently put in all the ELB (Electronic Logbook) entries for the various maintenance issues and then operations escorted us upstairs to debrief the Chief Pilot. In the moment; both myself and the CA felt okay and crew scheduling deadheaded us to ZZZ1 to rejoin our pairing; but in hindsight; I think it would have been better if we had finished the day and gone to the hotel in ZZZ as it was on the deadhead flight that I really started to feel the after effects of adrenaline wearing off.