Theres something horribly wrong, but, if the board is mis-reading what the processor is telling it, it could be going into this shutdown loop.
The possible cause, since the heatsink is cool to the touch, and the computer reports insainly high temps, and he had stuttering in game, is the IHS not making contact with the cores for some reason, but makes perfect contact with the heatsink, who knows, it could have been a crap job or faulty processor from the factory.
EDIT: It could be the thermal paste has gone bad, but, it shouldn't have as long as you never tried to re-use it for some reason... Always use new thermal paste, especially if the stock is wax based, which, I would hope intel would know to use a grease instead of a wax.