I don't see the connection between the PSU being underpowered causing CPU temps to go high. Just don't see it.
I don't have any kind of proper understanding of this problem, but I can confirm this is very possible as it just happened to me. I had an underpowered powersource for my rig with an FX 8320 that was reporting terminal 90c temperatures at start up. It has something to do with the voltage being inconsistent. Upgrading the PSU immediately fixed the problem.
And to be clear, in fact the processor wasn't overheating, which was verified by a much more knowledgable IT guy than myself who had the tools to take direct temperature reading of my processor and the socket during an "overheat to shutdown" event. The voltage was screwing with the processor's ability to gauge temperature. It seems to be more prevalent in processors which don't have actual sensors, like the FX 8320 though I do not know if this is unique to these types of processors but making sure your rig has a proper psu can absolutely fix this problem ASSUMING you're not experiencing genuine overheating. That s the first thing that needs to be confirmed here.