For what it's worth I think the problem may be exacerbated by using an external monitor and keeping the type cover closed on the surface pro 4 screen. The heat build up is far greater, and there was an occasion recently where the surface pro shutdown and there was an image of a thermometer on a blank screen.
Anyway, I can only use mine with an external monitor now - the Surface Pro 4 screen is kaput with the same problem everyone else has been reporting here. I have bought another Surface Pro 4 second hand (opened box but unused), and will be sure to keep the screen getting plenty of airflow.
I got the original in 2017, so 3 years of use. I just like them so much I had to get a replacement.