Thermal instability in a horizontal internally heated melt layer with a free upper surface and a solid-to-liquid phase change in the downward direction is considered. The critical Rayleigh number depends strongly on the ratio of liquid layer thickness, which contains internal heat sources, to melt layer thickness, and stabilizing temperature boundary conditions. It is found that the liquid layer is always stable when the stabilizing boundary temperature is larger than 0.3. The critical Rayleigh number decreases when melt rate (Stefen number) increases. The pattern of natural convection cell reveals that the melt layer will be carried upward to mix with the upper layer and to dilute the intensity of the internal source. Application to reactor safety, core disrupture accidents, post-accident heat removal, and radioactive waste storage, as well as thermal storage, suggests that estimation of downward heat transfer rate by conduction alone may lack conservatism and can cause significant errors.