Stat is thermostat yes.
If you did the stat is the fluid in the overflow tank up to level or low due to a small leak?

If fluid is ok, then Id suspect the stat. It came in the housing correct and you installed the whole assembly together?

The fan is not it if your driving and still hot as the forward motion will do sufficient cooling typically.

Let us know, Woody

BTW the overflow tank has a cap, when tight there is pressure in the system when warm. I suggested it be loose to allow you to check flow in the earlier post.