A321 Captain reported an engine over temperature during climb. The Captain retarded the power lever; the over temperature condition diminished; and the flight continued to the destination airport.

Narrative

On take off; near Vr the First Officer alerted me to the fact that the Right (#2) Engine EGT was starting into the red. We did not have any ECAMs or Alerts because I'm sure they were inhibited. We also did not notice any indications of compressor stall. While continuing a normal takeoff and climb out; I eased the Right (#2) power lever back just a little out of the FLEX position and the First Officer stated that the EGT returned to the green. The EGT was probably slightly in the red for approximately 5 seconds. I then eased the right (#2) power lever back into the FLEX position and the EGT remained in the green and we climbed out normally. The remainder of the flight the engine had all normal indications. After landing and parking at the Gate in ZZZ; I made a logbook write up and called maintenance. To be honest; I have no idea why the engine began to overheat. The temperature was warm outside for ZZZ1; but it wasn't extreme. And we were using FLEX thrust; not TOGA thrust! Maintenance needs to look at this engine to make sure it is preforming properly; so that it doesn't happen to another crew.