After some experimentation, I guessed it was because the game was trying to show me too many things on the turn transition - so what I did was to change to strategic view (F10) just before clicking "next turn", then the transition was quick and I was able to reach the next turn without crashing. I then changed back from strategic to normal view.
I didn't have to do it in subsequent turns, passing that turn everything seemed to go back to normal.
Your temps are mostly fine, maybe the CPU is a bit hot, if these are idle temperatures.
Seems like it's the RAM or the CPU.
GPU faults don't act up like that.
So, you setup an isolated stress test for each suspect.
RAM:
Download memtest86+ and install it on a medium and boot your system with it. I'd suggest USB key:
http://www.memtest.org/#downiso
If it passes the tests, move on to CPU.
If it doesn't, find and remove the faulty RAM stick and repeat the test.
CPU:
Download prime95 and run it, no need to reboot:
http://www.mersenne.org/
It might also be that your CPU is running too hot. In that case, open your case (warranty is lost, if any) and clean the dust off from the heat sink and the fans, if any. See if the temperatures drop. If not, the heat sink might have come loose, or has not enough contact to the CPU die. You might want to re-apply the heat conducting fluid.
Best Answer
Try opening the CD tray and closing it. The game then unhangs and continues as usual. You may stop hearing the music for a little bit, but it should restore and keep playing.
This trick is not very well known, but it helps with this specific game.