I've just stopped a five minute burn-in of FurMark, which is the most graphically intensive work this machine has done. Still no hang. I'm gonna try a Memtest and a HDD test, to disqualify them too. This is quite annoying
P.S.: It showed up on GPU-Z. Tops out @ 71C and stays there. Still no hang.
EDIT: OK, GPU-Z seems to be all over the place... now it stopped updating the temp @ 79C. Regardless - it doesn't hang even when GPU is stressed.
EDIT2:

Currently running Memtest. Finally got gpu-z to work properly and it survived 5 minutes of extreme burn-in @83C stable.
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CPU: AMD Phenom™ II X3 720BE
MB: Gigabyte GA-MA790X-UD3P
RAM: Corsair TWIN2X4096-8500C5D
HDD: Western Digital WD6400AAKS
VC: Sapphire HD4890 Toxic
PSU: Corsair HX620W
CASE: Cooler Master HAF-922