This paper reports on the development of a new application of the thermal probe in the determination of the thermal conductivity in non-linear problems. The method uses a direct non-linear numerical model associated with a parameter estimation technique to determine temperature dependent conductivities. Using enthalpy as the primary variable in the numerical model, phase change situations can easily be accommodated. The potential and effectiveness of the method are shown through test data obtained by simulated experiments. (c) 2007 Elsevier Ltd. All rights reserved.