<p>Although thermal transport in semiconductors is dominated by phonons, in certain polar semiconductors like GaN, the contribution of electrons to heat conduction is significant. In this paper, the distribution of temperature in a two-dimensional GaN computational domain subjected to a localized, pulsed electron source is simulated using the electron–phonon Monte Carlo (MC) method. Electron pulses are emitted out of the source terminal and carried by the electric field in the GaN two-dimensional electron gas (2DEG) channel similar to that of a high-electron-mobility transistor (HEMT). Electron and phonon temperature profiles associated with pulse propagation are monitored as they travel across the domain using the electron–phonon MC. The initial temperature profile obtained by MC is compared with the parabolic two-temperature model (TTM). MC simulations are performed for electron and phonon temperature profiles for different electric field intensities and pulse durations. The phonon temperature profile is found to mimic the shape of the electron temperature profile due to strong electron–phonon interaction (EPI), maintaining a notable time lag between them due to the difference in their group velocities. Other aspects including electric field dependence and time evolution for a given spatial region of temperature are also studied.</p>