A non-intrusive inverse heat transfer procedure for predicting the time-varying thickness of the protective phase-change ledge on the inside surface of the walls of a high-temperature metallurgical reactor is presented. The inverse method, used here as a virtual sensor, enables the on-line estimation of the position of the solid-liquid phase front using a heat flux sensor embedded in the reactor wall. The virtual sensor comprises a state observer (Kalman filter) coupled to a state-space model of the reactor. Three different virtual sensors are thoroughly tested: (1) an unscented Kalman filter with a nonlinear state-space model, (2) an extended Kalman filter with a nonlinear state-space model, and (3) a linear Kalman filter with a linear state-space model. Results show that the virtual sensor composed of the unscented Kalman filter yields the best results for the operating conditions that prevail inside industrial facilities. Its predictions are more accurate than that of the linear Kalman filter, more stable than that of the extended Kalman filter, and its CPU time requirement is comparable to that of the other sensors. (C) 2012 Elsevier Ltd. All rights reserved.