The authors proposed models of unsteady heat transfer processes related to dry surface formation after liquid-solid contact on superheated surface. These processes have strong relations with wetting initiation condition on high temperature solid surface cooled by boiling: i.e. transition point between low cooling rate by film boiling and rapid cooling rate by transition boiling. The proposed models include processes such as unsteady heat conduction in both solid and liquid layers, spontaneous nucleation near liquid-solid interface, and vapor bubble growth and packing. As known well, spontaneous nucleation rate of liquid dramatically increases at a certain temperature. In this paper, revised model is presented, where unequally spaced grid was applied in both liquid and solid layer near liquid-solid contact and the step number of generated bubbles by spontaneous nucleation was increased. Model calculations were done for water, ethanol and HFE-7100 as liquid, and Fe, FeO, Cu, Al and sapphire as solid materials. It was found that there was lowest limit of initial solid temperature when dry surface formation occurs, and the limit temperature strongly depends on the physical properties of solid and liquid. This limit temperature is considered to have close relationship with wetting initiation condition stated first. When compared to experimental results on wetting initiation of Fe-water combination, the calculation results show good agreements.