The temperature dependence of the heat conductivity has been obtained for a liquid crystal model based on the Gay-Berne fluid, from the isotropic phase at high temperatures through the nematic phase to the smectic A phase at low temperatures. The ratio of the parallel and the perpendicular components of the heat conductivity is about 2.5:1 in the nematic phase, which is similar to that of real systems. Both Green-Kubo methods and nonequilibrium molecular dynamics methods have been applied and the results agree within in a relative error of a couple of percent, but the latter method is much more efficient. (C) 2009 Elsevier B. V. All rights reserved.