Certainly sounds like a VRAM or GPU overheat issue to me, prob more likely the former.
Ideally you'd have a cheap PCIe video card laying about, so you could swap that in and see if the problem disappears. Then swap back in and see it come back. Something like this:
http://www.newegg.com/Product/Produc...82E16814150655
Tho saying that, I think your CPU has integrated GPU anyway so just removing the video card for a few days should be sufficient. (obv then need to conenct the monitor to on-board output)
Ideally you could find some way to trigger the problem. In the olden days I used to run 3dmark2001 (and later 2003?) on endless loop for a few hours on any build - that would almost certainly crash if there were problems with the GPU. I expect there is something similar these days, others ITT probably know better. Furmark perhaps?
http://www.ozone3d.net/benchmarks/fur/ Of course we'd also run memtest86 for a few hours first thing, before even putting the board in the case
Newegg should have easy RMA process, being such a popular retailer. Places with an awful returns process don't end up popular, I'd imagine!