I have an ASUS F2A85-M MB with a AMD A8-5600K APU with Radeon 7560D and have noticed the same different temperature readings with this CPU. However, what I didn't realise was what the MB fan controls were doing. I had repeated shutdowns during hot weather and when the windows 10 software was working hard. Using HWiNFO and checking the BIOS CPU fan control settings I found that the BIOS uses the sensors from the ASUS F2A85-M (ITE IT8603E)CPU readings and NOT from the CPU [#0]: AMD A8-5600K:Enhanced CPU (TSI) and CPU (Tctl) for the CPU Q-Fan Control. Coupled to this, the default settings of the fan and temperatures of the the CPU Q-Fan Control were way out so that basically the fan speed only really increased when it was far too late, causing an overheat and shut down. Yes, I can hear the CPU fan working a lot more now, but no random shutdowns. Also the CHA_Fan Q-Fan Control in the BIOS is linked to the MB temperature readings under the same package. I firmly believe the the Windows 10 package is working the CPU much harder than the original Win 7 package I was initially running.
I thought I would add this in case anybody else is having similar problems.