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This paper focuses on the thermal characterization of high power white light LED of 1W and 3W. Thermal transient method is used to measure the junction temperature and calculate the thermal resistance. The emphasis is placed upon the investigation of junction temperature in both the 1W and 3W LEDs for a limited range of drive-in current (500mA up to 1A) with the air velocity kept constant throughout the experiment. All investigations are based on the transient junction temperature measurements performed during the cooling process. The presented results include the cumulative structure functions and differential structure functions. It was found that the measured junction temperatures and thermal capacitances of both the LEDs increased with the input power (drive-in current). However, the thermal resistance decreased with the increase of drive-in current.