1) Temperature controllers use a sensor to measure temperature and compare it to a setpoint, sending an output signal to control heating or cooling elements to regulate temperature.
2) There are three main types of temperature controllers - on/off, proportional, and PID. On/off controllers simply turn heating/cooling fully on or off, proportional controllers vary the on/off time proportionally, and PID controllers combine proportional, integral and derivative control for the most accurate regulation.
3) Factors like the sensor type, output needed, control algorithm, and number of outputs should be considered when selecting a suitable temperature controller for an application.