Power supplies and power controllers are disclosed. A disclosed power supply has a power controller, a power switch, an auxiliary winding, a first circuit and a second circuit. The power controller is a monolithic integrated circuit with a multi-function pin and a gate pin. A control node of the power switch is coupled to the gate pin. The first circuit is coupled between the multi-function pin and the auxiliary winding and has a diode. The second circuit is coupled between the multi-function pin and a ground line, and has a thermistor.