If you get a powerdown due to heat issues, it is usually pretty systematic. You startup the PC and after approximately x time it shuts down.
Temperature protections are built into the BIOS and motherboard chipset. In modern boards, there are several overheat triggers in CPU, GPU and case.
Heat issues can also appear in such cases where BGA chips (typically GPU) have breaking solder joints due to thermal expansion. In these cases, again, the problems are often related to computer temperature. But I have not seen that eg. failing GPU causes shutdown.
What I do know however, is that faulty voltage rails (3.3V, +5V, 12V, -12V etc) that are giving wrong voltages will trigger safety shutdown in modern PCs… AND … come to think of it … so will short circuits in things like USB voltage rails.
Now, lets assume one of the decoupling / filter capacitors of one of these voltage rails is dying. That will lead to uneven voltage on one of the rails. If you get corruption on screen, it means the GPU is struggling to read memory clearly. This is turn can be because the logic level is uneven or too low - a condition that would soon trigger an emergency shutdown.
I advise to open up case and do a cleanup of fans and heatpipes. Also remember to check that fans are turning on, because faulty fans (no rpm signal) will also trigger shutdown on a modern PC