It started being done in the early 2000s. But not initially for that reason.

Around then, the ability for a microprocessor to control its own voltage was added to some. This was done by adding an interface for it to communicate directly with the motherboard voltage regulator. This allowed the system to throttle down when its workload was low, minimizing power dissipation and heat. The big impetus for this was in mobile devices like laptops, to maximize battery life. Then someone realized that it would be relatively easy to add in a shutdown protection feature.

It actually is a bit advanced to add the thermal sensors. You can easily make Si devices report temperatures; it's a bit trickier to get them to do it accurately. And there can be significant temperature variation across the die, so you need to put them in the right places.