Using the analogue of the electric inductance, we reveal the properties of the thermal inductance in GaN-based light-emitting diode devices by testing their transient thermal behaviors. We find that the devices exhibit a transient thermal response under step-down or step-up currents and observe notable inductive phenomena of the temperature response as time evolves from start up to some hundred microseconds. We define thermal inductance as the rapid change in device temperature that is opposite to the temperature change expected from the power input. These findings can promote new temperature measurements, and novel thermal analyses of high-frequency semiconductor devices that combining the thermal resistances, thermal capacitances, and thermal inductances.