of this model shows the power at
DE-461 1.3 5.0-2.5
1.3 amps at 120vac or 5amps at 12vdc or 2.5 amps at 24vdc
That AC and DC doesn't really add-up,
the question is how many amps at 20vac?
120vac to 24vac transformers are common for outdoor sprinkler systems.
Here is a 10amp unit for $30, 24V, 10A Center Tapped (12-0-12) Transformer | MPJA.COM
A simple relay will turn it on/off, use 12v to turn it on off.
Here is one rated 20amps $6
12VDC DPDT 20A Aromat Relay | MPJA.COM
Thermistors are used essentially as a resetable fuse, they cutoff when too hot.
I think maybe you are thinking of a temperature sensor to turn on/off the fridge based on the fridge temp right?
I just built a controller for the refridgerator in my soda machine,
I replaced all the analog controls with a microprocessor that has a LM34 temp sensor,
and used a solid state relay that is controlled by only 3v output from the micro,
this $10 6amp unit.
hope that helps.