The sequential function specification method together with the network simulation method were applied in the inverse estimation of the time-dependent heat transfer coefficient with internal heat generation. The thermal properties of the solid and air are dependent on temperature. The input data are the temperature history at a particular location of the solid. The common iterative least-squares approach is used to minimize the functional and in all cases a piecewise function is used to approximate the solution. Copyright © 2004 John Wiley & Sons, Ltd.