An empirically derived polytropic index for the solar wind is applied to two magnetohydrodynamic models of solar wind propagation. The first of these models is time-independent and can be used to define an initial solar wind state for the second, time-dependent model. The time-dependent model simulates the propagation of disturbances, such as shocks that originate at the Sun, through the interplanetary medium to Earth as a space weather forecasting tool. Both models assume adiabatic flow of the solar wind. Changes are made to these models to include the effects of heating of the solar wind by applying the empirically derived polytropic index. The adjustments made to the time-independent model produce a moderate solar wind state that compares well with Helios 1 data. Data concerning several shocks observed at the Sun and corresponding storm sudden commencements at Earth are used to investigate the predictions for shock arrival times made by the time-dependent model. Changes in the predictions for shock arrival times resulting from the application of the empirically derived polytropic index for the solar wind are discussed. ¿ American Geophysical Union 1996