A321 Captain reported returning to departure airport after the #2 engine overheated in initial climb.

Narrative

After takeoff at approximately 600 AGL number 2 engine exhaust gas temperature rose to over 700 degrees. After thrust reduction; temp went to between 605 and 620. ECAM number 2 Engine over temp flashed while temp varied. As we climbed; temp decreased; we as a crew decided not to shut down engine since temp was slowly decreasing. Although we did decide to return to ZZZ overweight in concurrence with Dispatch. Followed QRH for overweight landing and non-normal landing procedures. Landed without further incident.I was on 10 days of flying without ability to go home; received my break at hotel. Had somewhat good sleep; but was getting quite burned out from being gone for so long. Became a little overwhelmed once ECAM started flashing to shut engine down. Communicated to First Officer I was no longer in the green and he assured me he was in the green. Once we decided to return to ZZZ and followed all QRH procedures I returned to the green and felt less stressed and communicated to my First Officer. Landed without incident.