A model of the energy balance of the dayside ionosphere of Venus is presented. Calculations of the dayside electron and ion temperature profiles are carried out and compared with data from experiments on the Pioneer Venus orbiter. The coupled heat conduction equations for electrons and ions are solved for several values of the solar zenith angle. It is shown that thermal conductivities are inhibited by the presence of a horizontal magnetic field. A realistic model of the magnetic field that includes fluctuations is employed in deriving an appropriate expression for the thermal conductivity. The contributions of photoelectrons, ion chemistry, Joule heating, and solar wind heating to the energy balance of the ionosphere are considered.