Game overheating/turning off my computer

This is probably because of your graphics card pushing itself too hard to get the maximum framerate. The game hasn't been optimized yet, so it can be quite heavy. Turning Vsync on will cap the framerate at 60fp, but you may need to install a framerate limiter if you need to lower it further than that.

I'd also suggest cleaning out your PC fans if you haven't recently!

That is very strange. I'd suggest something like SpeedFan so you can control fans directly and monitor specific temperatures, as it may be some component other than the graphics card overheating?