Always go off what your Bios states. You could be looking at the CPU socket which tends to run 10 degrees or more hotter than the CPU 'cores'. If you download and install HWMonitor then you can see the temperatures of your CPU socket and core and determine them with what the other software record. But like I said Bios is the one to believe and your CPU is usually full load when in the Bios so 60 degrees is safe.
I ran a test. It showed 57degrees CPU and then 50 degrees processor temperature and tempin0 and 1 where matching the CPU and motherboard reading. Core reading was matching all the other programs.