I have a similar setup with similar results. I've purchased a GA-F2A88XM-D3H also running on a A6-6400K. When entering the BIOS I see the temp approaching 60'C within just a few minutes. And that doesn't seem right at all. (Scythe Shuriken SCSK-1100 cooler). The BIOS settings are "Optimal default", no tweaks. The problems with this is my fans are whining like crazy. That's not much fun for a HTPC in the livingroom...
Have you had contact with Gigabyte about this? I'd be very interested in their response.