I would suggest RMA. It's most likely got a heat issue. It shouldn't have issues like that. Your CPU shouldn't be shutting down the whole PC because of the GPU. The fan on keeping the system from crashing tells me is a great issue. What manufacturer do you have?
OC wouldn't make a difference right now. I asked about OC because if you didn't have enough voltage, you could get a crash.
I can't find any other reason why you'd shut down like that. I think it's GPU crash from heat. The fan is supposed to kick on around 60 degrees C by default settings.
Go to Event Viewer. Windows Logs. And it should be under System, but check the others in case. There should be something related to your crashes. Take a look and see what is there.