Whether its at 33C or 38-45C those temps are perfectly fine. In fact really good especially for an 8350. The motherboard you have will do just fine for the 8350 although it is not recommended to get below a 990FX based motherboard. (You have the 970 chipset) There seems to be no problems at all. On an anecdotal note, I used to own the 8350 myself. The first motherboard I had for it was the Asus M5A88V-EVO. It was definitely NOT made for the 8350 (in fact it was an update to an older board originally meant for regular AM3 CPUs) and yet it still ran with no problems.
I think you'll be just fine with what you have now.