It seems to me like a faulty PSU or CPU. Your temperatures are extremely high for a neutral PC. I'd probably get that checked out with the solutions said above.
You can't really use hwmonitor to check your psu voltages.
Again until you stress your computer 100% you'll not know if it's a load issue, or a intermittent failing part issue.
As for a "Liquid" cooler, they're useless on a stock cpu.
I'll check the cooling forums for any suitable CPU cooling options.
However I did check the PSU voltages with a digital voltmeter and everything was normal.
Also, I stressed the CPU with the software you gave me. CPU temps went over 80°C but surprisingly nothing happened. I had to stop the program because I wasn't sure if it was going to fry it.
Could it be a RAM problem? I tried memtest86+ and after 10 minutes of testing the computer switched off.
That software is meant to push the PC and hardware in order to stress test it. Let it run for a bit (3-5 min or so?) as testing temperatures via UDK and Minecraft isn't really reliable.
UDK can take up quite a bit of resources, but really depends on how much is on screen and what it is doing. Minecraft isn't demanding at all.
The program won't fry your CPU. The CPU will auto-shut off if it starts to reach unsafe temperatures, hence the shut down.
I'm ASSUMING , you hit near 100C, that is your cpus max temp.
It really should be able to run 24/7 at 100% and stay around 80C. I do this with mine as I run folding at home, and so it runs 100% 24/7 and it's been that way for over a year.
While the temp might not be your shutdown issue, you do have a problem, though I'm thinking it is because you have a crappy case for air flow.
If you can not run prime for at least an hour with out your temp going over 95C you need to think about getting a new case for the parts. Liquid cooling like a Corsair will be wasted money.
What memory test are you doing? Memtest is the best as it is a bootable program that RUNS LINUX and can test everything.
Memtest86+ - Advanced Memory Diagnostic Tool
I think you may be correct it is not a heat problem but you do have a problem with heat.
Yha, that case is horrible for air.
You may even be overheating your psu.