An inverse model is presented for determining the strength of the temporal dependent heat source when the prior knowledge of the source functions are not available in the two-dimensional heat conduction problem. This model is constructed from the finite difference approximation of the differential heat conduction equation Based on the assumption that the temperature measurements are available over the problem domain. In contrast to the traditional approach, the iteration in the proposed model can be done only once and the inverse problem can be solved in a linear domain. Three examples are used to show the usage of the proposed method. (C) 1997 Elsevier Science Ltd.