Spinodal decomposition of a very viscous binary mixture is simulated, assuming that the fluid is bounded by two walls that are instantaneously quenched below the critical temperature. As usual, the mixture phase separates by forming dendritic structures whose size grows with time. While in conventional spinodal decomposition the morphology of the mixture is isotropic, here we show that, when the two components of the mixture have different heat conductivities, the configuration of the mixture may become anisotropic, depending on whether heat propagates slower or faster than mass. Specifically, for large heat conductivity differences, when the Lewis number is small, dendrites tend to align parallel to the isothermal lines; when it is large, dendrites progressively align perpendicular to the isothermal lines. This behavior can be explained observing that the morphology of the mixture is the result of two competing effects: on one hand, the mixture phase separates as soon as its temperature reaches its critical value and therefore it tends to follow the isothermal lines; on the other hand, the system tend to maximize heat transport, and therefore dendrites tend to span between the two quenched walls, i.e. perpendicular to the isothermal lines. This explanation is confirmed showing that when the imposed temperature difference between the side walls (and therefore the heat flux at equilibrium as well) is increased, dendrites tend to align across the walls more and more. (c) 2008 Elsevier Ltd. All rights reserved.