What you can do to relieve your GPU from overheating is disabling realtime rendering (top left menu in the viewport). That option should be off by default in my opinion, having it sit at full speed all day must kill any GC eventually.
I think 97° C shouldnt be too hot for a GPU, arent modern ones maxed at 130° or something? And do GPU’s switch off a PC when they overheat? I though the display driver would stop it, wait and restart itself, not bringing the PC down.
Shader compiling brings my CPU to the highest temperature any program ever lead too (>80°). If it were just a bit more and my PC would switch off too. You are certain your CPU’s core temperature doesn’t rise too high? There are several temperatures measurable and or offsetting the reading might be wrong.