Cell disturbances such as alumina feeding, anode effect, metal-tapping and anode changing often cause variations in the heat balance of a reduction cell, resulting in deviations from the optimum operating conditions. A dynamic thermal model built on an earlier one-dimensional simulation by the authors had been used to solve the transient heat conduction with phase change in the sidewall/ledge region. An improved model based on a moving finite difference method was developed to simulate the dynamic ledging behaviour. Fixed-grid and deforming-grid spacings were respectively superimposed on the sidewall and ledge region in order to track the moving front. Various aspects of the process dynamics with respect to the variation of ledge thickness and sidewall shell temperature were considered.