The past six years has seen a tremendous growth in scanned probe microscopies of various sorts. In this letter, we add a new capability to this family-mapping of thermal conductivity variations on a nanometer scale. We show how our new probe technique can be used to measure thermal conductivity of conductors and thin insulating films deposited on top of conductors. Our results also demonstrate for the first time, the capability of the technique to image subsurface details of samples. As the thermal conductivities of different materials can vary by over three orders of magnitude, we suggest this as an important new contrast mechanism for studying materials on the nanometer scale.