Need thermostat

I am trying to fix a little Peltier fridge. It seems to work in its entirety except there is no heating or cooling.

My assumption is the thermostat no longer works. Is this a piece I can purchase locally? Would anyone be able to tell me more accurate search terms to replace this part?

A quick look at Mouser shows:
In the far right column click on “thermostats” and then on “apply filters”.
Need a part number and / or some idea on how it responds to temp changes.

That’s a Bi-metal switch. Do you know the rating?

There is a sticker on thew back of the fridge that says 38W -45W when in use. That’s all the info I can find except the B10 stamp on the switch.