Just tested a Pi Zero running the HD Video Player setup, with the device in Power Save mode and heated it up with a hairdryer whilst refreshing the device info page.
I got up to a recorded temperature of 81.51 degrees C before I decided I’d given it enough torture, and the content ( HD video files @ 1920x1080 60hz ) continued to play without any issues.
So whatever the previous issue, I’m now confident that it wasn’t due to the heat.