First you need to realize that BF4 is not the same 'coding' method Dablio 3 is nor even BF3, as it now uses the CPUs much more intensenly then either of those games, so it isn't something to say "I Play Duke Nukem for hours and BF4 should also be on Ultra with no problems". In your case of your problem, I am offering a attempt at some solutions, and asking for feedback when testing them. As I said I suggest throttling back the BF4 graphics levels and see if that helps resolve it first, and second instead of worrying about the CPU temps what are your GPU temps?
My reason is a point you wish to debate, so let me put it bluntly (http://techreport.com/forums/viewtopic.php?f=12&t=89356
http://pclab.pl/zdjecia/artykuly/chaostheory/2013/10/bf4_beta/charts/bf4_cpu_radeon.png http://www.youtube.com/watch?v=5Cj8RP4kEGo and so on) all show that a i7 Core works better then a i5 or i3, and definately better then any AMD Cpu because of hyperthreading. AMD CPUs can ONLY and repeatedly get to i3 Core levels, with higher / expensive end AMD CPUs (like yours) achieving i5 levels as the max. Thus on a i5 or a AMD, you should play at HIGH not ULTRA graphics on BF4 to avoid causing issues (series FPS drop, BSOD, overheating, crashes, lock ups, etc.).
Further the scores for a 770 (http://www.bf4blog.com/battlefield-4-retail-gpu-cpu-benchmarks/) are playable (40s to 50s FPS) when PAIRED to a i7 Core, so with your CPU you can see the FPS drops even significantly more / pushing too hard - overheating, and back to my question on the GPU temps????
As ONLY BF4 has this issue (according to your last response) please try throttling back the graphics level first, this is the MOST COMMON test / resolution for majority of people. If you keep dropping it and get to low graphics say 1280x1024 display (minimum) and your STILL having the issue, then there is another hidden underlying issue that is just adding to the overall problem.