Pilot reported a Green Hydraulic System Overheat ECAM Message after take off. The flight crew secured the Green System Hydraulic Pump and monitored the system. The flight continued to destination airport where a normal landing was expected.

Narrative

Approximately 15 minutes after departure; Green Hydraulic Overheat was annunciated via ECAM. Procedures followed; with system pump placed to off. Follow-up procedures also completed. First Officer and I discussed best course of action. A declaration of emergency to ATC was not warranted given the abnormal condition; in our opinion. Pan-Pan-Pan was offered to ATC; requesting a change in routing; keeping us closer to suitable diversion airport should further issue(s) develop. This request was honored. Overheat condition abated approximately 30 minutes into the flight. To allow for additional cooling; engine driven pump was not reactivated until near ZZZ1. Monitoring the hydraulic page of ECAM; system pressure returned to normal; overheat did not reappear and flight continued for normal landing ZZZ. Dispatch informed me of one; or more; events of same issue has occurred. Dispatch was utilized to relay updates between flight; maintenance and ZZZ; including possible need for stop on runway and towing to gate. Once system remained in normal condition; Dispatch et al was informed; as was ATC; a normal landing was expected.