Temperature is an important parameter in motor operation. Temperature can indicate any abnormality before any serious damage occurs. The two temperatures which are monitored at the bearing temperatures and the winding temperature. 
Winding temperature is measured by temperature sensors which are attached to the windings in the stator slots at the time of manufacture. These temperature sensors are not always accessible from outside. The sensors (usually RTDs) can be connected to any external monitoring device.
Abnormal winding temperature in a motor winding can indicate overloading or poor ventilation. Poor ventilation can be due to a filter which has choked. High ambient temperature can also be a reason for high winding temperature.
Abnormal winding temperature can cause damage to the insulation eventually leading to failure.
Bearing Temperature
Bearing Temperature in motors is measured by temperature sensors which are machined in the bearing housing such that the tip of the sensor comes in contact with the bearing. These sensors are also connected to the temperature monitoring equipment.
High bearing Temperature can be caused by improper alignment with the load, inadequate lubrication and even high ambient temperature.
In some motors, temperature gauges or industrial thermometers which indicate temperature are provided. Readings from these instruments can be periodically taken and monitored.
In smaller motors, no temperature monitoring provision is given. If any abnormality is suspected, non-contact thermometers can be used to measure the temperature.