This paper describes a new two-dimensional method for study of GaAs Schottky-barrier MESFET's. A modified form of the conduction current is used in which transport properties are described in terms of electron temperature rather than electric field. Nonequilibrium velocity effects such as velocity overshoot are included. Results for the one-dimensional GaAs diode and the two-dimensional GaAs MESFET are presented and compared to other studies that utilize the Monte Carlo procedure. Larger values of current cut-off frequency are predicted for submicrometer gate length MESFET's than in previous two-dimensional simulations which utilize the steady-state transport properties.