Removing the thermal fuse. For testing purposes you can temporarily bypass the thermal fuse to see if the fan runs.

Rebuilding A Fried Fan Motor Hackaday
Fan motor thermal fuse. You can also choose from thermal low voltage fan motor thermal fuse as well as from fuse cutout other home appliance parts fan motor thermal fuse and whether fan motor thermal fuse is high or low. To make fuse replacement easier we need to free the motor from the control unit keeping its wiring harness as long as possible. This happen soon or later for any fan. A failure to start may be caused by faulty start windings in the motor. A check of the continuity of each of the coils led him to this thermal fuse. The thermal protector consists of one or more heat sensing elements built into the motor or motor compressor plus an external control device.
In both cases the motor can not cool down using part of the air draft it created. Disconnect power to the fan before proceeding. When the motor seized the ac current built up a lot of heat. Its possible and perhaps even likely that the capacitor failed causing the motor to not spin and that caused the windings to overheat. The thermal fuse will remove power when the motor becomes burning hot. Either dust prevent cooling or the bearing or the equivalent get wear out so much that the fan rotate more slowly.
This fuse is made to burn out before a fire can. In some fans the fuse is hidden inside one of the short fiberglass sleeves gold color bundle in the picture that cover the connections between the motor windings and the control wires. The thermal protection is present to turn the motor off when excessive heat is generated within the motor circuitry. A wide variety of fan motor thermal fuse options are available to you such as iec csa.