A thin liquid film resting on a solid substrate that is heated or cooled from below experiences surface tension gradients, which lead to Marangoni flows. We explore the behavior of such a film on a chemically patterned substrate which drives film dewetting in order to determine how surface patterning and applied temperature gradients can be designed to influence the behavior of thin-film coatings. A nonlinear partial differential equation for the film height based on lubrication theory is solved numerically for a broad range of problem parameters. Uniform cooling of the substrate is found to significantly delay dewetting that is driven by wettability gradients. Uniform heating speeds up dewetting but can destroy the near-perfect templating imposed by the surface patterning. However, localized heating and cooling together can accelerate dewetting while maintaining templating quality. Localized heating and cooling can also be used to drive liquid onto areas that it would dewet from in the absence of heating. Overall, these results indicate that applied temperature gradients can significantly influence dewetting driven by surface patterning, and suggest strategies for the creation of spatially patterned thin-film coatings and flow control in microfluidic devices.