This paper presents a methodology, based on the Reciprocity Function approach, for the estimation of a two–dimensional thermal contact conductance in a transient three–dimensional heat conduction problem. Thermal contact conductances appear on the contact surface between two materials that are put in contact, due to the presence of some irregularities in such interface. The technique presented in this paper allows to estimate the heat flux and the temperature jump, both on the thermal contact interface, leading to the estimation of the thermal contact conductance. In the proposed technique, temperature measurements can be taken non-intrusively on the external surface of the materials. The method gives good estimates, even when noisy measurements are considered.