The only BIOS update is a beta BIOS update as of right now for 12th gen see here for details 12th Gen Intel Core BIOS 3.06 Beta you cannot downgrade from 3.06 beta → 3.04 BIOS if I remember right so consider that.
Regarding the clocks my guess is that the clocks are spiking in these light loads and the heat output with it. It is something that I noticed with my 11th gen and now I power limited the CPU until I need the extra resources.
You might want to validate the thermal system is working as expected by comparing your system to others with benchmarks, there are several user benchmark post on the forums and even an official FW one.