Motivated by the need to understand how external fields influence the stability of dynamic contact lines, the linear stability of gravity-driven spreading of a thin liquid film in the presence of electric and temperature fields is studied. The film is confined from below by a flat substrate and from above by an air gap and another flat substrate. An electrostatic potential difference or temperature difference can be applied between the two substrates and the liquid is taken to be a perfect dielectric whose surface tension decreases linearly with temperature. Traveling-wave solutions are found for the film profile, and both electric and temperature fields influence the height of the capillary ridge of liquid that forms near the advancing contact line. The linear stability analysis shows that electric fields destabilize the film front to transverse perturbations and that temperature fields can either stabilize or destabilize the front, depending on the direction of the temperature gradient. An energy analysis reveals that the electric field in the capillary ridge is most responsible for the enhancement of the perturbation growth. For the case of temperature fields, the perturbed temperature gradients are the dominant mechanism through which the perturbation in film height is affected.