PC shutdowns certainly can be temps, PC restarts could also be a power supply voltage issue for example.
A game cannot cause a computer to shut down , it may be trigger for another issue though
Are you certain temps are not the cause ? swtor does make a very good thermal test on a system
Press the windows key and type reliability and see if anything is listed in the reliability history.
provide a dxdiag per this link , can see what crash reports are listed too
Also are you overclocking the machine in any way. Run it at stock and see what happens as well as what wombleninja suggested.
