Heat transfer between a hot, semi-infinite plate and thin liquid film flowing over its surface is considered. As the plate is semi-infinite, the finite cooled portion of the plate and the temperature at the moving film front are time variable. The heat transfer is transient, as opposed to the usual quasi-steady process that exists when the plate is infinite. To investigate the transient heat transfer, solutions describing the temperature fields of the wet and dry portions of the plate are conjugated at the moving film front. The basic characteristics of transient cooling process are found to be governed by a dimensionless parameter named the Leidenfrost number, which is the ratio of the Biot number and the square of the Peclet number. The plate temperatures at the moving front, the film velocity, and the time required to reach the wetting temperature are calculated.