The coupled, one-dimensional electron and ion energy equations, with a combination of small steady and fluctuating horizontal magnetic fields imposed, are solved for the Mars ionosphere, corresponding to conditions encountered during the Viking mission. A series of calculations with various boundary conditions and heat sources result in a range of electron and ion temperature profiles, which are compared with the results obtained by the RPA's carried aboard the Viking landers. It is shown that solar EUV heating alone does not lead to the observed temperature profiles and that assuming reasonable heat fluxes at the top result in good agreement. It is also found that the introduction of small steady and altitude dependent fluctuating horizontal magnetic fields, which modify the thermal conductivity, leads to electron temperatures in reasonably good agreement with the RPA data, but does not match the observed ion temperatures above about 240 km. The effects of chemical and Joule heating are also examined and found not to be significant. ¿ 1998 American Geophysical Union