A composite of two or more thermal interface materials (“TIMs”) is placed between a die and a heat spreader to improve cooling of the die in an integrated circuit package. The two or more TIMs vary in heat-dissipation capability depending upon the locations of die hot spots. In an embodiment, a more thermally conductive material may be positioned over one or more die hot spots, and a less thermally conductive material may be positioned abutting and/or surrounding the more thermally conductive material. The two or more TIMs may comprise a solder and a polymer. The composite TIM may be preformed as one unit or as a plurality of units. Methods of fabrication, as well as application of the package to an electronic assembly and to an electronic system, are also described.