Battlefield 3 PC black screen with sounds

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.

I had the same problem on Windows Vista 64-bit. After some Googling, I found nothing but I did notice that people with Windows XP did not have the same problem. Anyways, here's my solution:

For Windows Vista/7 users, you'll need to run the game in Windows XP Service Pack 2 emulation mode. Navigate to your Steam CoD installation: C:\\Steam\steamapps\common\call of duty Right-click on CoDSP.exe and click Properties In the Compatibility tab make sure the "Run this program in compatibility mode for:" is checked and change the drop-down to Windows XP (Service Pack 2) Hit Apply and the OK

After this, I was able to change the brightness from in-game without a problem. If this still won't help, try running it as an Administrator. You can follow the above steps but the checkbox is further down in the Compatibility tab.