GPU Overheats and game crashes

Are you overlocking?

Running the factory GPu settings, max fan speed. The card is an msi variant which is tuned up from the factory.

It doesn't seem to slow or speed up how long it takes it to crash whether it's on max gfx or min.

This on DirectX 11 or 12?  

Assuming you're correct in that the gpu is failing, this happens somewhat often with factory over clocks, it's a bad clock job.  You need to either tune it down, or up the voltage(I'd tune it down, these guys typically run hot to begin with) to fix your stability issue.  Ashes just happens to be the first game working it hard enough to trigger the flaw.  It's possible you have a bad heat sink seating and need to fix that instead, but monitoring software should tell you your gpu is getting radically overheated.  Install a tweaker if you don't have one already, and check the problem out.  Odds are you can achieve a stable card with less than 50mhz down on the core clock, a negligible performance loss.

Are you certain the GPU is overheating? If it's a factory overclock, I suggest acquiring the factories "tuning" utility that can alter voltages, clockspeeds, etc. and UNDERclocking the GPU enough Mhz to get it to the reference speed. If the card works when underclocked, call the mfr for an RMA. I have zero issues doing the same with EVGA. I've had stellar support from them and they keep getting my dollars.

Otherwise, inspect your case closely to be certain the intake and exhaust fans are actually working on your case. Crack it open and clean it with a vacuum and/or take it outside and blow it clean with some compressed air.

One way to help test whether it's truly an overheating problem would be to take the side of the case off and point a desk-type or similar fan directly into the case and see if you can still recreate the results.

Good luck and let us know how it works out!