Does the system stay on if you enter the BIOS? If so, perhaps you may be able to monitor the temperatures and fan speed.
Otherwise, you may test motherboard out of the case in a non-conductive surface with the minimum components and also test the video card in a different system. In case the issue persists, you will probably need to swap the motherboard or the CPU with a different one in order to narrow the cause further.
I hope this helps.