We study the self-heating effect in a high-power AlGaN/GaN High Electron Mobility Transistor (HEMT) grown on silicon. We determine the HEMT static channel temperature using a dc characterization method and the results are compared with values calculated with a two-dimensional thermal model. No experimental data on the dynamic thermal behavior are available until now. For this reason, the transient thermal response on current pulses in the sub-microsecond range is estimated theoretically by means of a three-dimensional thermal model.