The thermal energy transport in semiconductors is mostly determined by phonon transport. However in polar semiconductors like GaN electronic contribution to the thermal transport is non-negligible. In this paper, we use an electron–phonon Monte Carlo (MC) method to study temperature distribution and thermal properties in a two-dimensional GaN computational domain with a localized, steady and continuous electron heat source at one end. Overall, the domain mimics the two-dimensional electron gas (2DEG) channel of a typical GaN high electron mobility transistor (HEMT). High energy electrons entering the domain from the source interact with the phonons, and drift under the influence of an external electric field. Cases of the electric field being uniform and non-uniform are investigated separately. A two step/temperature analytical model is proposed to describe the electron as well as phonon temperature profiles and solved using the finite difference method (FDM). The FDM results are compared with the MC results and found to be in good agreement.

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