Did you upgrade to Win10? If so, check your motherboard/PC manufacturer's support page of their website for Win10-specific drivers. If you upgraded from Win7, still check their support page for their recommendations on Win10 as they may only have Win8 drivers but recommend them for Win10 (hope that made sense).
Otherwise, sounds like a classic temperature problem. Make sure all your fans are running properly. We all assume they're spinning but visually check. This game works the GPU harder than the CPU so it could easily be a GPU overheating problem, not a CPU overheating problem.
Crack open your case and inspect to see how clean it is. Clean it and any fans as necessary. While you're in there, check that everything's seated and connected firmly. Also, you could try opening the case and pointing a fan directly at the guts inside your case, run the game hard, and see if that helps.
These should be good places to start.
Good luck and report back!