In recent years, the measurement technology of local thermophysical properties becomes more important. In this paper, we propose the new local thermal conductivity measurement method, Contact Temperature Method, in which thermal conductivity of sample is calculated from the contact temperature between a probe and sample. In the experiment, we tried to measure the thermal conductivity of glass under Au thin film for the contact thermocouple electrode with Pt wire probe. Measured data shows that thermal conductivity of nonconductor under thin metal film can be measured when the thickness of film is less than one-thousandth of the contact radius. However, thermal conductivity of bulk material could not be measured correctly. Therefore it is necessary to construct a new thermal resistance model in consideration of oxide film, distance from contact point to temperature measuring point and so on.