The effect of van der Waals forces on the fingering instability of a thin liquid film wetting a solid substrate and moving under the action of a thermal gradient applied along the film is investigated. Both horizontal films and films climbing a vertical wall are considered. A linear stability analysis shows the stabilizing action of the van der Waals forces. The effect of gravity forces can be either stabilizing or destabilizing, depending on the relative strength of the effects of gravity and surface-tension gradients. A weakly nonlinear analysis of the unstable wetting front shows that the frontal evolution is described by the Kuramoto-Sivashinsky equation, revealing the possibility of chaotic behavior of fingerlike patterns near the instability threshold.