Combinatorial methods offer an efficient approach for the development of new materials. Methods for generating combinatorial samples of materials, and methods for characterizing local composition and structure by electron microprobe analysis and electron-backscatter diffraction are relatively well developed. But a key component for combinatorial studies of materials is high-spatial-resolution measurements of the property of interest, for example, the magnetic, optical, electrical, mechanical or thermal properties of each phase, composition or processing condition. Advances in the experimental methods used for mapping these properties will have a significant impact on materials science and engineering. Here we show how time-domain thermoreflectance can be used to image the thermal conductivity of the cross-section of a Nb-Ti-Cr-Si diffusion multiple, and thereby demonstrate rapid and quantitative measurements of thermal transport properties for combinatorial studies of materials. The lateral spatial resolution of the technique is 3.4 microm, and the time required to measure a 100 x 100 pixel image is approximately 1 h. The thermal conductivity of TiCr(2) decreases by a factor of two in crossing from the near-stoichiometric side of the phase to the Ti-rich side; and the conductivity of (Ti,Nb)(3)Si shows a strong dependence on crystalline orientation.