The reading in the BIOS is not the core temp, but the socket temp. It's not as accurate as the core sensor so allow for that when figuring out thermal headroom. You might be able to read it in Windows with the unlocked processor using Open Hardware Monitor.
No, core temps are disabled when you unlock the cores, there is no application that can 'turn that on'.
The best you can do is socket temp, which is still OK.
You just need to lock the CPU again, check the temps the core reports, then check the socket temp, and then you know how off the socket temp is. Use something like CPUID HWMonitor, or AMD's overdrive utility or something like that.
That way, when you unlock the cores again, you have a better estimate of the true temps.