A simple, two-dimensional, spectral model of heat transport in the Venus ionosphere has been constructed. Numerical experiments with the model suggest that a nocturnal heat source about an order of magnitude smaller than the day-time source is required to simulate the observed ion and electron temperatures. The solar zenith angle dependence of the high-altitude ion temperature appears to be caused by expansion followed by compression of the plasma as it flows from the dayside to the nightside. Thermal-flux saturation appears to be significant on the nightside, but the formation of a standing shock wave does not seen to be required to explain the broad features of the observed, nocturnal ion temperature.