An X100 machine that old, there's a good chance that the heat sink grease is worn out. It turns dry and powdery with age and stops doing its job. Then the CPU overheats, and the thing starts crashing. Have you seen any video artifacts? That's one of the first signs of overheating, but it doesn't always happen.
Anyway, carefully remove the heat sink from the CPU, clean off the old heat sink grease (probably a powdery residue) with something like rubbing alcohol (the alcohol/water stuff, don't use anything with detergents, moisturizers, colors, etc.) and apply a tiny dab of new grease. Then replace the heat sink. Be gentle. Too much pressure can crack the somewhat fragile CPU package.