I think they are both getting cooked, CPU and GPU. Please look at the screenshot I posted below (same as yesterday, Intel Power Gadget). The strange thing is, that the CPU frequency stays very low in fullscreen mode - even lower than in windowed mode, although the CPU consumes 3x the energy and heats up quickly. I have no idea how this is possible and why. At the same time, in fullscreen mode, the GPU frequency is as high as it can be (it is the green GT graph). The difference here between windowed and fullscreen mode does not seem a lot, but the GPU is clearly running at 100% in fullscreen mode all the time.
I also attached two screenshots of Macs Fan Control - one before and one after a few seconds of fullscreen mode (main menu, just looking at the buttons again and not doing anything). The CPU increase is about 40 C° and the GPU is 37 C°. Even the SSD gets a little hotter, but that might be due to the whole system heating up.