The aft-gap formation between the casting and the metal mold during the casting of metals creates a thermal resistance that reduces the heat transfer and solidification rates. In this work, the on-line inverse solution methodology based on the kalman filtering technique and the recursive least-squares algorithm is developed for estimating the variation of unknown contact conductance with time from the temperature measurements taken with thermocouples at the outer mold surface. From computer simulation studies, we have demonstrated the effectiveness of this method in estimating some typical cases with time-varying contact conductance. The scheme is simple in concept and reduces the computational load in implementation drastically. The applications can be extremely useful in efficient and immediate identification of unknowns such as period contact conductance or heat flux.