My 2 cents says it's the thermostat.
If you got a cheap "poppet" style from a local supplier for like 5 or less. Rip it out and get a good "Sleeve" type. The sleeve type can flow more and have a smoother modulating transition, this keep the temperatures even. Vendors like Summit or Jegs show them as a "heavy duty or Hi Performance" piece. I usually see them for like 8 to 10 bucks.

And welcome to CHR too! Nice seeing you here.

OH! one more thing.. pictures are always most welcome.