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Thermal transient testing is widely used for LED characterization, derivation of compact models, and calibration of 3D finite element models. The traditional analysis of transient thermal measurements yields a thermal model for a single heat source. However, it appears that secondary heat sources are typically present in LED packages and significantly limit the model's precision. In this paper, we reveal inaccuracies of thermal transient measurements interpretation associated with the secondary heat sources related to the light trapped in an optical encapsulant and phosphor light conversion losses. We show that both have a significant impact on the transient response for mid-power LED packages. We present a novel methodology of a derivation and calibration of thermal models for LEDs with multiple heat sources. It can be applied not only to monochromatic LEDs but particularly also to LEDs with phosphor light conversion. The methodology enables a separate characterization of the primary pn junction thermal power source and the secondary heat sources in an LED package.