One of the challenges in constructing global magnetohydrodynamic (MHD) models of the inner heliosphere for, e.g., space weather forecasting purposes, is to correctly capture the acceleration and expansion of the solar wind. In many current models, the solar wind is driven by varying the polytropic index so that a desired heating is obtained. While such schemes can yield solar wind properties consistent with observations, they are not problem-free. In this work, we demonstrate by performing MHD simulations that altering the polytropic index affects the properties of propagating shocks significantly, which in turn affect the predicted space weather conditions. Thus, driving the solar wind with such a mechanism should be used with care in simulations where correctly capturing the shock physics is essential. As a remedy, we present a simple heating function formulation by which the polytropic wind can be used while still modeling the shock physics correctly.