The process of freeze coating of a polymeric melt onto a two-dimensional flat plate moving continuously in the axial direction is simulated, taking into account the limited heat capacity of the plate, the spatial variation of the plate temperature, and the heat converted from the melt to the freeze coat. To identify the controlling parameters in the process, the system of equations governing the plate temperature and the shape and the temperature of the freeze coat is transformed into dimensionless coordinates. Numerical methods have been used to solve the resulting mathematical model. The history of the spatial variation of the shape of the freeze coat is presented in graphs. The parameters controlling the shape of the freeze coat are identified, and it has been found that the plate-coat diffusivity ratio, a convective heal transfer parameter, Péclet number, Stefan number, and the fusion temperature of the molten fluid are the parameters that control the growth and decay of the Freeze-coat layer. The effect of these parameters and the boundary conditions on the behavior of the freeze-coat process is discussed.