An analytical model for falling-film wetting of a hot surface has been developed to account for the effect of cooling by droplet-vapor mixture in the region immediately ahead of the wet front. The effect of precursory cooling is characterized by a heat transfer coefficient decaying exponentially from the wet front. Based on the present model, the wet front velocity, as well as the temperature profile along a thin slab, can be calculated. It is demonstrated that the precursory cooling can increase the wet front velocity by an order of magnitude. Existing experimental data with variable flow rates at atmospheric pressure are shown to be successfully correlated by the present model.