In this work, a hybrid simulation technique is introduced for the electrothermal study of a twodimensional GaN-on-SiC high electron mobility transistor. Detailed electron and phonon transport is considered by coupled electron and phonon Monte Carlo simulations in the transistor region. For regions away from the transistor, the conventional Fourier's law is used for thermal analysis to minimize the computational load. This hybrid simulation strategy can incorporate the physical phenomena over multiple length scales, including phonon generation by hot electrons in the conduction channel, frequency-dependent phonon transport in the transistor region, and heat transfer across the whole macroscale device. Published by AIP Publishing.