I've heard these gigabyte boards have faulty sensors. If you touch the heatsink, does it feel hot or warm? I had my cpu running at 50 degrees before and it felt luke warm on my heatsink.
Over 60c, that sound bad at idle. Well re-install that cooler. Clean surfaces. Apply uniform paper thin thermal paste and mount the cooler snuggly. Them measure temps again. If it's still at 60c then touch the HSF, at 60c the bottom part of the cooler it should be hot to your touch. If so then it's really at 60c if not then the sensors are crappy.
Yes, Gigabyte have that temp sensor problem as the same with my GA-8N SLI Royal board. It's not giving me accurate temps. So I use other softwares but still not good temps. I got a drive bay temp sensor to accurately monitor the temps of my cpu.
Leave the system off for a while, long enough for it to cool to room temp.
Turn on, get in the bios, check the cpu temp.
If the cpu temperature goes up crazy quick, then it's most likely the hsf is not installed correctly.
TAT doesn't lie... that's what the chip uses to decide whether to throttle. Try rotating your heatsink 90 degrees.
BIOS sensors usually are onboard temp sensors, not on-chip die thermistors.