Previous experiments revealed some unusual behavior of wetting films driven across inclined surfaces by thermal gradients. Below a certain threshold film thickness, the film, predictably, formed a bump that was stationary but subject to a fingering instability. Above the threshold the bump was, unexpectably, stable but nonstationary. This new structure was identified by Bertozzi, Munch, and Shearer as that of an undercompressive shock. In this study we investigated the extent to which their proposed model, dealing with infinite films spreading across infinite, ideal substrates, can be applied to real systems of finite dimensions. It was found that while the velocity and width of the bump were not subject to finite size effects, the profile of the bump was not accurately predicted by the model.