I will have to give this a think.
Just seems strange that the breaker blows at the same time independent of the temp cycle.
Without a wiring diagram I do not know how they are regulating the temperature. If the cycling thermostat only has two wires I would replace that one first.
Before replacing the breaker again I would shut off the mains and make sure the wires going to the breaker are tight and installed correctly. I would also open up the wall receptacle and check it's connections and the wire connections at the terminal block in the machine.
Hopefully someone else will jump in with a couple more ideas.