B747-8 flight crew reported engine fire during climb out. Flight crew returned to departure airport and landed uneventfully.

Narrative

On climbout; with the First Officer (FO) as the pilot flying (PF); passing through approximately 3000 ft. we got an OVHT ENG 2 NAC EICAS message; immediately followed by a FIRE ENG 2 warning message; as the FO engaged the right autopilot. I requested priority handling with ZZZ Departure and requested vectors back to the airport. We were instructed to level off at 4000 ft. and cleared back to ZZZ via radar vectors for Runway XX. I ran the checklist; and engine #2 was shut down; one fire bottle was discharged which extinguished the fire warning after approximately 15 seconds. We were asked for souls and fuel (both quantity and time) onboard; as well as if we were carrying hazmat. Once the checklist was finished we ran through our normal flow of checklist and procedures in preparation for landing. After being vectored for the ILS Runway XX; the landing was uneventful. We taxied off Runway XX on taxiway 1 and we're instructed to turn left on taxiway 2 and stop if able. The fire trucks were waiting for us and after being inspected we were cleared to taxi back to the spot under escort by fire truck. Once in our parking spot I filled out the maintenance log with the discrepancies and we then deplaned. Engine fire caused the subsequent engine shutdown and air turn back.