A light-emitting diode (LED) device includes first and second LED dies with the same structure and that are both encapsulated by the same silicone layer. The first LED is supplied with sufficient drive current to illuminate the LED. Control circuitry supplies the second LED with a constant current, determines the voltage across the second LED, and calculates the temperature of the second LED based on the voltage across the second LED. The constant current has a maximum magnitude that never exceeds the maximum magnitude of the drive current. The LED device is able to calculate the temperature of a diode with a gallium-nitride layer (GaN or GaInN) that is receiving a large drive current and emitting blue light by determining the voltage across an adjacent similar diode with a gallium-nitride layer through which a small constant current is flowing. Preferably, the band gap of the LEDs exceeds two electron volts.