New PC with RX 480 - Freezes during DirectX 11 games! ARGGGHH!!!

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Could also be related to the PSU - the longer you play, the greater the power-draw, which could lead to a crash. I had that happen with a R9 290 (Granted, that card uses more watts, but still). What PSU do you have?
 
Just because the CPU can reach such high temperatures doesn't mean that you don't have a problem with the CPU that the paste shouldn't fix. There is really no reason why the temp should be that high.
 
Ok I'll try applying new paste to lower the temps. PSU is Corsair 650M.

[strike]As for the card after playing Fallout 4 a DX11 game for hours straight without freezing I'm concluding that the graphics card is fine. The games that froze - Stranded Deep and The Forest are both alpha's so the problem is probably with the game code.[/strike]

update: Wrong! Since upgrading to a modern monitor it freezes in FO4 as well as many other games.
 
I recently upgraded to a modern monitor, my previous monitor was run at 1024x768 because the drivers were that old they didn't support 64 bit OS. Now I've got a 24" 1080p monitor running FreeSync at 144Hz and I've tested more games at this resolution.

Fallout 4, Pro Farmer 2017, Ark Survival all freeze to a grey screen after playing for a short while (at 1920x1080 144Hz, high to ultra detail) when CPU temps hit 71oC or above which is supposedly the maximum temp for the CPU according to Intel. But when it freezes the GPU fans are spinning at 100% and still continue to after reset until Radeon Settings starts up again at which point it says "Default settings restored due to an unexpected system failure" then the fans slow down.

Just because the CPU can reach such high temperatures doesn't mean that you don't have a problem with the CPU that the paste shouldn't fix. There is really no reason why the temp should be that high.

I've tried removing the old paste and reapplying new paste but have not received any noticeable improvement in temps. If there is no reason for the temp to be that high and it's not the thermal paste then what could it be? The motherboard power supply cable doesn't click in due to the clip not being long enough to contact the notch, might that cause CPU temp to increase? The case has one fan on intake at the front so it's positive pressure, power supply is mounted on the bottom.

Make sure that you wipe the paste completely. Watch a youtube video for that. It is easy. Buy a market cooler also. I recommend you to buy a Cryorig h7 or Cooler master hyper 212 evo or a Thermaltake frio silent 14.

I have been looking into coolers and the Cryorig h7 seems to have a reputation for being an excellent cooler. I am just about to buy one but why do I need one when the CPU shouldn't be getting that hot in the first place? I thought coolers are generally only needed for overclocking CPUs aren't they?

How can I find out what's causing it to freeze the GPU or CPU?