This work reports the development of a measurement technique for the estimation of thermal contact conductance at a polymer (Nylon)-metal(Copper) two dimensional interface having an annular contact under low external loading. The experimental setup consists of a vacuum chamber capable of achieving a pressure of 10−6 mbar. The chamber is fitted with electrical, thermocouple and fluid feed-throughs. Two dimensional temperature measurements are performed on the top surface of the polymer sample away from the boundary interface and are used to estimate the thermal contact conductance at the interface. The estimation process is accomplished by solving an inverse heat conduction problem using artificial neural networks coupled with Genetic algorithm. The actual pressure distribution at the annular Nylon-Copper interface is measured using a pressure sensitive film and the variation and the distribution of contact area between the mating surfaces is shown. The estimated values of thermal contact conductance obtained using the developed non-intrusive technique are found to be in good agreement with those reported in literature. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.