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What resolutions and settings is that. Also what software did you record it with?
Isn't the 280X basically a 7970 with higher clockspeed/minor adjustments? Looking it up it's essentially the gigahertz edition. Bloody impressive for a 5 year old GPU, and speaks volumes about the optimisation work DICE put in for such a good looking game.

I get like 40 deg on idle (with one screen) and I get between 65-75 when playing CS:GO (everything on low at 1080p, fan at 100% when I hit 70) even though the GPU usage is around 50%. To be fair, my case is one of the smallest available. 
To be fair the GTX680 copes quite well with BF1, my brother still using the one I sold him for it. He uses the memory usage limiter to avoid going over 2GB, is 3GB enough for 1080P in this game? I'm not trying to start another RAM argument here, just curious.