Air carrier Captain reported receiving an aircraft generated GPWS Terrain Warning after takeoff from an airport with mountainous terrain and hot weather. Crew complied and flight continued uneventfully.

Narrative

Takeoff clearance given with on course approved. After take off complied with the ODP (Obstacle Departure Procedure); which was straight ahead till an altitude until turning on course. During the turn reached 1000 AFE (Above Field Elevation) and 'climb sequence' was called for. Flaps were raised on schedule in the turn. As the flaps were raised the aircraft climb rate reduced to 200-300 fpm climb triggering a GPWS Terrain caution for rising terrain around the airport. The turn was shallowed to and aircraft climb rate was increased and the caution cleared quickly. On course was achieved and climb rate continued to increase with no further GPWS alters.Cause: Very close to max Runway take off weight departure and hot ambient temperatures. Even though the ODP was complied with and flaps were raised on schedule consideration for the hot temperatures and heavy weight was not given in conjunction with a turn. This caused a moment where adequate climb performance was not achieved. Suggestions: Hot and heavy conditions; while expected and are normal for this time of year; will need more consideration. The expectation that one complies with an ODP and flaps retraction speeds doesn't guarantee absolute clearance of terrain; especially when combining climb performance limiting items (hot; heavy; turn - increased load factor; etc). Consideration of these would have lead to waiting more time between flap retraction; turn initiations to allow the aircraft to maintain climb rates.