Three-dimensional (3D) packages are of considerable interest at the present time as a means for heterogeneous high-performance integration of disparate digital, analog, optical, and MEMS technologies. However, their design is challenged by several issues, including the appropriate choice of thermal solution to be used in the 3D stack. Suboptimal placement of heat sources/sinks leads to hot spots, which are detrimental to package reliability. The broad goals of this study are to determine the appropriate cost and reliability-constrained heat-sinking solutions through an optimal placement of spatially distributed energy transporting elements. The heat-sinking solutions considered in this study include microchannels, and thermal vias. We conduct a microchannel analysis to develop a reduced model of the heat and mass transfer characteristics of the microchannel. We also develop optimization techniques and tools for thermal solution design of three-dimensional packages. We use a nonuniform “real-life” microprocessor power map for the illustration of the procedure. We subsequently obtain the optimal size and location of the thermal vias and microchannels in a 3D stack by minimizing a proposed multi-objective criteria. Finally, we develop and illustrate the notion of design maps that would guide the designers in the selection of appropriate thermal solution technologies for 3D packages.