HD7870/Corsair CX600M PC rebooting issue

Hello,

Specs:
MoBo - Gigabyte GA-880GM-UD2H
CPU - AMD Phenom II X4 965 3.4GHz
RAM - Kingston Hyper-X blu, 8GB
GPU - Radeon HD5770(old test)/Sapphire Radeon HD 7870 GHz Edition
HDD - 466GB Seagate
PSU - Corsair CX600M

While playing games with said HD7870, my system has begun to restart itself, no error message just cuts out then reboots. At first I thought it was the processor overheating however the temperatures never
exceed 70C on load.

I ran 'MdSched.exe', but no faults were found with the RAM.

So I decided to switch out, back to my old HD5770 and after somewhat extensive
replaying on my old GPU the problem did not present itself. I then changed back
to the 7870 and the problem returned, I tried adjusting the fans to 100% to rule
out overheating as a cause but still the problem presented itself.

By process of elimination I'm assuming it's the power supply/GPU relationship, however from what I can tell it's got the 7870 covered in regards to both wattage requirements and amperage, so I'm not sure why.

Could it be motherboard related in any way, or am I just being stupid?

Any help is appreciated as I'm stumped. Thank you for your time.

With regards,

Ed Barnard

P.S. Sorry if this is posted in the wrong subforum