If the system is shutdown during loading into windows, then it could be HAL issue since you replace new board on system using same hard drive which has OS installed. If it is a case, you should run repair installation that should solve the issue.
If system shutdown while still in bios page (POST), then possible causes from many: memory, PSU, motherboard issue, etc. The way you explained in question is likely the heat issue. Even you applied thermal paste between cpu and heatsink, but if you could try again: clean them, apply new thermal paste, try that see if it helps first.
If you have more than 1 memory stick, remove one at the time see if system acts same problem?
You should also fo minimal setup (less hardware installed on system, only basic components) see if it works better?
You could also, remove the board out of the case, place on cardboard and test it.
