I also recently replaced my heatsink and thermal paste; when I originally installed the heatsink I had done a horrendous job of adding thermal paste, and was getting frequent crashes. Reapplying the thermal paste properly solved a ton of issues.
Here are some examples:
I ran prime95 after fixing my heatsink and had it running for around 3 hours with no issue. I booted up Assassin's Creed IV, played it for a bit, closed the program, browsed the internet, opened up a youtube video about twenty minutes later and the computer blue screened.
Immediately after the previous problem, I allowed the computer to restart, attempted to reopen a youtube video, and the computer bluescreened again.
Another day, I had had my computer on long enough to redownload Assassins Creed IV as I intended to install it onto my SSD to fix a potential issue I've been having with the game hanging every 30 seconds or so for a few frames each time. Upon attempting to install the game once it finished downloading, the computer bluescreened while installing DirectX.
I restarted the computer, installed the game with no issue, and it bluescreened again around a half hour later.
Yet another day I was playing Assassin's Creed IV for about six hours when it bluescreened suddenly (which wiped my progress; UPlay cloud saves are fantastic)
Yesterday I played Skyrim for around three or four hours after the computer had been on around three hours and it bluescreened on me.
I'm not really sure what the problem is - the computer seems to be fine and stable and working because it'll run for hours with no issues. I also don't get a warning prior to the crashes; there's no sound stuttering, problems with framerate tearing or anything. The system will just up and crash and seems to keep crashing for a while afterwards. The computer is well ventilated, the temperatures are all low and stable, and I'm honestly at a bit of a loss. What can I do to diagnose the issue?