I put my money on Motherboard - sorry
Either you're experiencing BIOS bug connected with CPU VRM regulation or simply VRM's are dying.
Still, changing PSU seems to be the easiest option to try first! Good luck!
The problem with this theory is that a dying VRM would crap out under load, not just under idle. As for a BIOS bug, I'm on the latest (and last) BIOS for this motherboard (Asua P67 Sabertooth)...I could downgrade as there is a procedure for this. That procedure does carry a non-zero chance of bricking.