I have also experienced this. I've only had the P2 H3-3D combo up in the air once since the gimbal install, but even while installing / testing, it would get very hot.
I assume it's somewhat normal? Have you received any other responses?
I have exactly the same problem. This is not normal. I have H2-2D same size and shape and I don´t have similar problems with same gopro, I have Zenmuse Z15 and other gimbals and no hot camera problems...
I know gopro get hot inside his closed protection box after recording non-stop for more then 10 minutes but never so hot like this. I only can fly 1 battery and after that it is impossible to touch my back gopro gimbal plate.
Dji Phantom v2 + H3-D3 v1.0 and Gopro all with last firmware installed.