Hi! I had the same exact problem as you. Everything froze all the time, with no spikes of temperature and no error messages, not even in the log. Tried to fresh install Windows 7 and 10 about 5 times, swapping my SSD for a HDD with no luck.
So I swapped every single part of my rig with a whole other AM3+ system I had on hand, and it turned out it was my FX8350 that was acting up. As soon as I put it in the other system the whole thing just froze completely, while my PC with the other CPU was running completely fine. In the meanwhile I even bought a new mobo, but turned out to be useless. So I RMAd the CPU and got a replacement about a month ago, but even if it was WAY more reliable than before, it still crashed once or twice again.
Turned out my PSU was also bad (fryed my GPU, lucky me), even if the PSU tester was indicating a very steady voltage. I got my new PSU 4 days ago and no crashes yet even if I intentionally make my computer run 24 hours and reboot it every once in a while (fingers crossed).
So long story short, RMA your CPU if you are still under warranty, it may be irreversibly damaged, and check very closely your PC for any PSU-related problems. I'd even think about like a preventive RMA for it.
Good luck
PC specs:
AMD FX-8350
Gigabyte GA-970A-DS3P
Asus GTX970 Strix
Antec HCG-750M
16gb DDR3 Corsair Vengeance
Adata SU-700 128gb SSD
WD Black 1TB HDD