A computer shutting down from overheating does not mean there is an issue with the CPU, it actually is a sign that everything is running well. It creates an automated shutdown to prevent any damage from happening, and overheating usually occurs well after the POST runs so the CPU wouldn't have any reason to prevent it from running.

Sounds like a case of over heating, let it sit for a bit then try using it again problem should go away, if it comes back you should bring it in to the shop to get the parts checked but I don't think that's the case.