No, it fits inside the winding space, and has wire leads. There are a few varieties of them, some look like a small metal fuse with wire ends, and need extra sleeving, while others look like a small dipped ceramic capacitor, typically black or white, and are designed to have the long leads sleeved and the wire soldered to them with a heat shunt to keep it from melting. Some in this style are self resetting, in that they, like the microwave oven ones, have a small bimetal disk inside that will pop to an alternative shape when hot and opens a set of contacts.
Yet more are PTC thermistors, that rely on having a hyperabrupt change in resistance over a certain temperature range, going from around 10-100R under a certain temperature, changing to 100K plus when the temperature exceeds a setpoint by around 5C. Others are a variant on the standard polyfuse, with them responding to either overcurrent by self heating or responding to high temperature inside heating them up to the transition point where they change to a high resistance state, and those rely on the self heating at high temperature to keep them high resistance till the equipment cools and they go back to low resistance again.