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A calculation of the electron velocity in heavily doped GaAs has been performed. A model to account for the LO phonon-plasmon coupling effects is proposed in a full Monte Carlo simulator; we believe this is the first time this fact has been tried out. Nonequilibrium screening effects are considered in the simulation. The Pauli exclusion principle is extended to the hot electron regime by the use of the electron temperature, which is calculated self consistently from the mean energy. A direct comparison with experimental velocities is made to show the accuracy of the simulation at both 77 and 300 K. Comparisons with simpler Monte Carlo models are also presented to illustrate the influence of the different effects considered.