I have read different methods for pulling the thermostat and the brass ring that holds it in place. Apparently CAT makes a puller for it. Here is what work for me:
I tried boiling the entire assembly but after that the ring would not budge. I then placed it in the freezer for the night. Next morning I had success with ( what I call ) a snap on crows foot pry bar ( part # 1250).
I was able to pry on the ring while the assembly was in a vice. The ring "walked" out, and the t- stat did the same thing.