A flyback power converter includes a transformer which has a primary winding, a secondary winding, and an auxiliary winding; a power switch controlling the conduction of the primary winding; and a control circuit generating a control signal to control the power switch, wherein the control circuit is an integrated circuit having a current sensing pin for obtaining a current sensing signal of a current through the power switch. The flyback power converter further includes a temperature-sensitive resistor or a mode detection resistor coupled between the auxiliary winding and the current sensing pin. The temperature-sensitive resistor provides a temperature-related signal for the control circuit to perform an over-temperature protection, or the temperature-sensitive resistor provides a mode detection signal for the control circuit to determine an operation mode of the flyback power converter.