Some relays have sensors which measure the temperature and send an actuating signal when the temperature crosses setpoint. Some of these relays are direct-operating, such as the bimetallic discs used to protect many small motors. These discs are warped to have two stable configurations, snapping from one to the other when the bimetal heats and cools. 
This causes the contacts to open and shut down the motor. If the contacts are in the control circuit (instead of the power circuit), the device fits the usual meaning of a relay.
Other thermal relays are "replica" relays, passing a current proportional to the current being monitored through a resistor with the thermal inertia replicating the time-thermal characteristic of the device being protected. These relays are used to protect the rotor bars of large motors. The overload heaters used in the typical magnetic motor starter are also a type of replica relay.
The actual temperature in large motor windings can be measured by embedded temperature sensors whose resistance changes with temperature. They can be used in an external electrical bridge circuit to provide an operating signal for the protective device. An auxiliary relay or electronic power amplification can be used to provide enough power to operate the device.
