A321 First Officer reported they received an Engine Number 2 'overtemp' indication following by a warning around 1;000 feet AGL during takeoff. The crew followed ECAM instructions and shut down the engine followed by a return to the departure airport.

Narrative

Shortly after takeoff we received a master warning with a #2 engine overtemp indication. I was the Pilot Flying (PF) and began a left hand turn in accordance with our departure instructions while the Pilot Monitoring (PM) analyzed the situation. The indication turned to a warning; directing an engine shutdown around 1;000 ft. AGL. I continued flying and we chose to keep the engine running as long as it produced thrust until terrain was no longer a factor. Fortunately it had been an APU on takeoff so that was running the entire time. The Captain [requested priority handling] with ATC; requesting vectors and a safe altitude to level at. They vectored us in a box pattern over the field and had us climb to 7;000 ft. MSL. Around 4;000 ft. we executed the ECAM instructions for engine shutdown. The aircraft was trimmed and autopilot coupled. It was a VFR day. The Captain continued running cleanup items and subsequent checklists to prepare for a return to ZZZ. The Dispatcher sent us numbers for an overweight landing. The Captain briefed the Flight Attendants (FA) and talked to the passengers while I set up for the approach. ATC was very helpful with vectors and giving us time to handle [the situation] before talking on the radios. Approximately 20 minutes after we shut down the engine; I began the approach. We landed without incident and stopped for Airport Rescue and Firefighting (ARFF) to inspect the exterior. They noted nothing abnormal so we taxied; and they followed us to the gate. Passengers deplaned. Scheduling called and asked us if we were OK to fly again once we had a good airplane. Union and the Chief Pilot called to check on us. The Chief Pilot made the decision to have us deadhead home; and cancel the scheduled turn afterwards. Both the Captain and I realized that was 100% the correct decision once the adrenaline wore off.Cause - The aircraft had several writeups for overtemping; and was even scheduled for an engine change that evening. It should not have flown at an airport with demanding conditions...extreme temperatures; altitude; terrain; and a max load.Suggestions - See causal factors above. Aircraft scheduling must consider repeat writeups and under-performing aircraft.