What's this thing in a peltier cooler?
It's a thermostat, originally known by the Klixon (now Sensata) name. They are based on a bimetallic disk, which is why they are cylindrical. 

Some types have a reset switch (a button in the center of the hidden side in your photo) and do not automatically reset, but most are simple thermostats with a fairly wide (maybe 5 to 15 degrees C) hysteresis. Below is a photo of a resettable type with mounting ears from this website: 



They are rather common in consumer appliances- cheap, simple and rugged.