Hi everybody, I have the exact same problem.
I even replaced my Surface with another one via telephonic assistance, to find that even this new unit has the same problem.
By my experience, I can tell that the problem presents only when the Surface is connected via AC plug; running on battery gives me almost no problems.
The only times when I have problems of black screens and HeatCore.dll errors even on battery is when I'm showing my screen on a video call, no matter the software I'm using (MS Teams, Google Meet, Zoom...): if I use the pen in this particular setup, sooner or later I'll get a black screen (again, also in this situation, running on battery reduces the crashes).
Hope to help someone with my experience and hoping even harder in a solution by Microsoft (seriously Microsoft, I don't want to use an overpriced iPad to write my notes for University)