The two-dimensional Laplace integral transform technique has been applied to get the spatial and temporal temperature distributions in both the molten layer thickness of a thin film coated on a substrate, the still solid part of the thin film of the target and the temperature distribution in the substrate. Also a formula for the time dependence of the evaporated part and the molten layer thickness of the thin-film as a function of time were obtained. The derivation has taken into account the temperature dependent absorption coefficient of the irradiated surface and the chemical reaction in the vapor of the thin film. Calculations of the obtained relations were carried out during the irradiation of aluminum thin film coated on a glass substrate with a pulsed laser