A321 pilot reported an Engine #2 Over Temp on take off. The flight Crew ran the checklists and QRH and performed an in flight shut down of the affected engine. The flight Crew requested priority handling and performed an air turn back and precautionary landing at departure airport.

Narrative

After take off from ZZZ; Runway XXR; ZZZZZ SID; experienced engine 2 Over Temp. ECAM directed (over ZZZZZ1 departure fix) engine shutdown was completed. All QRH and Company manual procedures were executed successfully and conducted overweight landing at ZZZ. Taxied to gate after landing. Upon return to gate after event; I learned from ZZZ Maintenance Personnel that the engine that overtemped on take-off was scheduled to be replaced later that same day; due to recent repeated over temp conditions. Due to high density altitude and critical terrain surrounding ZZZ; most take-offs during the warm months require a max take-off power setting. Scheduling an aircraft with an engine that is known to exceed temperature limits and therefore needs to be replaced to such a performance critical airport is in my opinion definitely a contributing factor. Although I understand there are approved allowances for aircraft with degraded engines to continue to operate under specified guidelines; I believe it would be in the interest of the safety of everyone to limit aircraft with identified performance issues from operations in and out of highly performance critical airports. Any takeoff weight above max landing weight creates additional concerns. As in the case of our departure from ZZZ; the ECAM directed engine shutdown did not occur until our SID departure path had already taken us past and away from the point where the specific Company published Runway XXR engine failure SID starts (we were about at ZZZZZ1 on the ZZZZZ SID). That procedure is designed to provide protection from terrain in case of engine failure. Since our path was beyond where we could safely turn towards the published engine out SID path; I believe it would be appropriate to have an identified decision point for where to disregard the engine out SID; and an alternate procedure for terrain avoidance.