Evolution of high performance microprocessors has resulted in a steady decrease in on-chip feature sizes. Increasing requirements on maximum current density are expected to increase interconnect temperature drastically due to Joule heating. As interconnect dimensions approach the electron mean free path range, effective conductivity reduces due to size effects. Thermal characterization of sub-micron interconnects and thin films is thus highly important. This work investigates current crowding and the associated Joule heating near a constriction in a thin metallic film and proposes a novel technique to determine thermal conductivity of thin metallic films and interconnects in the sub-100 nm range. Scanning Joule Expansion Microscopy (SJEM) measures the thermal expansion of the structure whose thickness is comparable to the mean free path of electrons. Numerical solution of heat conduction equation in the frequency space is used to obtain a fit for effective thermal conductivity. A thermal conductivity of ∼ 80.0 W/mK provides a best fit to the data. This is about one-third the bulk thermal conductivity of gold, which is 318 W/mK at room temperature. Using Wiedemann-Franz Law a thermal conductivity of 92.0 W/mK is obtained after measuring the electrical resistivity of the metal line. This is close to that obtained through numerical fit.