I don't know why your computer rebooted with the first settings. The High Quality setting wouldn't run in a less stressful way. Your dual core machine is going to be running pretty much flat out when encoding high definition video. And its going to be doing it for many hours on end, as you have noted.
You might want to monitor it every time you do any video encoding. And you should probably run a memory test to see if you have any issues there. Windows Memory Diagnostic is one free program for this, but Memtest86 + is more widely used by computer enthusiasts.
If you don't have too much compression to apply, and you are shooting for a 25gb target, I'd use either the High Speed (BD-25) option or the one pass CRF option. Your output size is going to be around 23.3gb, so use these settings when your original size is 30gb or less. When you set it to Automatic, the program tends to pick one of the fast encodes, and you were probably using the Good, 1 pass ABR setting. And I always keep the program in Idle Priority.
You should realize that the tests I've seen using the X264 encoder show a marked improvement in quality using a two pass encode. But you have to examine individual frames to see this most of the time. If you're going to the trouble of reencoding HD video, you might as well get good quality results, which is the rationale for using 2 pass encodes, but depending on the size of your screen, you may never be able to tell the difference between a 1 pass CRF and a High Quality 2 Pass while the movie is playing. The biggest problem with the two pass encode is that it takes longer, and with your dual core, this may tie up your machine for a very long time.
You can speed up the process a little bit by using two different hard drives...one for the source and one for the target. And you'll need two different physical drives, not just partitions on one.
Once you get over 30gb on the original file, you might want to consider doing a two pass High Quality encode. See how long it takes on your machine.
The X264 encoder can make good use of extra cpu cores, so upgrading to a quad core machine makes sense if you are going to be doing a lot of these encodes. That will be the biggest jump you can make in encoding times.
The temperatures you were seeing were actually pretty good for full speed video encoding, so it makes me think the shutdowns were not temperature related.