A model of the energy balance of the dayside ionosphere of Venus is presented. The coupled energy equations for electrons and ions are solved numerically and the calculated temperatures are compared with temperatures measured by instrumentation on the Pioneer Venus Orbiter. Neutral and ion density profiles consistent with those measured by various Pioneer Venus experiments are used in the model. It was found that using standard EUV sources and thermal conductivities the calculations produce temperatures that are much lower than the measured ones. Consequently, further calculations were performed in which 1) the thermal conductivities were inhibited by means of an almost horizontal magnetic field and/or 2) heat inflow into both the electron and ion gas at the top of the ionosphere was assumed due to the solar wind interaction. It was found that the calculated and measured temperatures were in reasonably good agreement if the thermal conductivities were inhibited by a near horizontal field of about 10 gammas and if the electron and ion heat fluxes were taken to be 4¿109 eV cm-2s-1 and 4¿107 eV cm-2s-1, respectively.