I don't know if it's related, but I'm getting similar issues - however, my PC does not reboot but just freezes and audio loops the last 0.5 seconds of audio. I can play at 720p for decent amounts of time, but even then its crashed after 4 hours or so.
I've had a similar issue before, when my GPU was fried, however that happened in all games. This is only in Fallout.
I've run all the regular fixes and test, other than swapping my GPU out to test it, but given that it's only in one game, I think it's a driver/game issue overall.