While I'm not sure what more info you are looking for, your pastebin seem to provide your answer. There are several logs that show high CPU temps. The BIOS will shut the computer down if the CPU's get to hot to protect them from burning out. The overheating could be caused by several things:
- The CPU fan could be dirty or not running at speed
- The case fan could be dirty or not running at speed
- If it is a laptop, the vents tend to get clogged with dirt and hair
- The heat-sink on the CPU could be dirty and clogged
- The thermal compound between your CPU and the heat-sink could be old and dried out so it is not transferring the heat like it should
In short I would appear from your logs that the system is shutting down due to overheating. The fact that this only happens when you are doing CPU intensive programs also strongly suggests that (in fact that was my first thought before I read your pastebin)
You can likely clean it yourself if you're careful: clean the outside vents with a dry toothbrush. If you open the case make sure that you don't have any static buildup on your body (touch something metal to discharge it), as any static electric spark can fry electronic chips. The best way to clean the inside of the case is with air, most stores sell canned air just for this purpose in the electronic section. If you use an air compressor, make sure the pressure is turned way down. Blow air into the fans and the heat-sink until the dust and hair is gone, make sure to blow off the motherboard afterwards, to clean off any dust you blew onto it. Just make sure that the power is OFF before you open the case — I recommend unplugging it!!
If the computer is old enough that the thermal compound is bad, you can buy one of those at electronics stores, but if you are unsure that you can replace it, I would recommend letting a shop do it for you. If it is done wrong, at best the problem will continue, at worst it could kill the CPU.
I realize that this doesn't answer your question, but it may solve your problem. I'm not sure there is one: if the system shut down due to overheating, I'm not sure you would get much more info that a hardware error, and that you are already showing in you posted log...
In fact the post you linked to says just that in the accepted answer:
Recently I had a system that started repeatedly to power off
ungracefully, turned out that it was overheating and the mobo was
configured to just power off early. The system didn't have a chance to
save logs, but fortunately monitoring the system's temperature showed
it was starting to increase just before powering off.