Monte Carlo based calculations of the large-signal nonlinear response characteristics of GaN-Al1-Ga1-xN high electron mobility transistors with particular emphasis on intermodulation distortion (IMD) have been performed. The nonlinear electrical transport is treated on first principles, all scattering mechanisms included, and both memory and distributed effects built into the model. The results demonstrate an optimal operating point for low IMD at reasonably large output power due to a minima in the IMD curve. Dependence of the nonlinear characteristics on the barrier mole fraction x is also demonstrated and analyzed. Finally, high-temperature predictions of the IMD have been made by carrying out the simulations at 600 K. An increase in dynamic range with temperature is predicted, due to a relative suppression of interface roughness scattering.