We have developed a quantitative model, based on a two-dimensional finite difference enthalpy method, which accounts for the localized melting behavior of thin Si films on substrates. The model incorporates radiative and conductive heat flow components and takes account of the phase changes that occur during zone-melting recrystallization. Emphasis is placed on the effects resulting from the differences in reflectivity and emissivity between solid and liquid Si. The model provides quantitative information concerning the temperature profile of the Si film and the configuration of the solid-liquid interface. Results of the analysis indicate that there exist two distinct types of transition behavior: i) reflectivity-change dominated and ii) emissivity-change dominated. Partial melting and a nonplanar solid-liquid interface are characteristics of the reflectivity-change dominated behavior. The emissivity-change dominated behavior, on the other hand, can be characterized by explosive-like melting and a planar solid-liquid interface. The conditions and physical factors which give rise to these behaviors are discussed.