An inverse phase change heat transfer method has been developed for predicting the time evolution of banks covering the surface of refractory brick walls inside high temperature smelting furnaces. The presence of these banks is indispensable as they serve as a protective barrier against the highly corrosive slag, thereby maintaining the structural integrity of the furnace and prolonging its active life. The numerical model rests on the conjugate gradient solution method with the adjoint equation. It predicts banks thickness and motion relying on the thermal conditions prevailing outside the furnace and temperature measurements taken at one location inside the brick wall. Simulations are carried out to examine the effect of different parameters on the predictive capabilities of the method. Results reveal that the method remains accurate in spite of the fact that the temperature measurements inside the wall are noisy and are taken at depth of few centimetres only. An example showing how the present inverse method can be used to warn on the imminent loss of the protective bank during the operation of a smelting furnace is then provided. (c) 2006 Elsevier Ltd. All rights reserved.