first, I'd watch dmesg from boot, to see if something useful pops up:
open a console and type
watch -n 1 "dmesg | tail -n 40"
to watch the last 40 lines that are reported by dmesg (some distros will require you by default to be root to do this, so if you get an error, try that)
Also, you may find information in system logs:
A traditional (non-systemd) distro will store text files under /var/log - often /var/log/messages is what you're looking for - you can watch the tail as above:
tail -f -n 40 /var/log/messages
If your system is running systemd, you would do:
journalctl -f -n 40
(again, you may need to be root to do this)
I recently had lockups that seem to have been thermal in nature - there weren't a lot of related messages - just once I saw something about hitting thermal limit, but that was a bit before the lock-up, so I dismissed it as just the behavior of modern cpus which run full-tilt until they reach thermal throttling. The machine was sent in for repair and had liquid metal thermal paste re-applied, and temps are down by about 10 degrees - really not that much, and temps are still sitting in the 90s, but so far, over the last 1.5 days, no lockup, but I'd need to run for a while longer to verify.