Fluid models for the auroral electron acceleration processes have almost exclusively been derived by assuming cold or isothermal electrons. The consequences of these assumptions have never been thoroughly analyzed. In this study we compare results from an isothermal simulation with those obtained when the pressure is calculated from a double adiabatic approximation and from stationary kinetic theory. We find that the reflection of shear Alfv¿n waves, as well as the current-voltage relation, is very sensitive to the description of the electron pressure variations. Using pressures calculated from steady-state kinetic theory, we find that driven shear Alfv¿n waves can build up auroral currents and fields that are consistent with a linear current-voltage relation.