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As modern electronic devices are increasingly miniaturized and integrated, their performance relies more heavily on effective thermal management. In this regard, two-phase cooling methods which capitalize on thin-film evaporation atop structured porous surfaces are emerging as potential solutions. In such porous structures, the optimum heat dissipation capacity relies on two competing objectives that depend on mass and heat transfer. Optimizing these objectives for effective thermal management is challenging due to the simulation costs and the high dimensionality of the design space which is often a voxelated microstructure representation that must also be manufacturable. We address these challenges by developing a data-driven framework for designing optimal porous microstructures for cooling applications. In our framework, we leverage spectral density functions to encode the design space via a handful of interpretable variables and, in turn, efficiently search it. We develop physics-based formulas to simulate the thermofluidic properties and assess the feasibility of candidate designs based on offline image-based analyses. To decrease the reliance on expensive simulations, we generate multi-fidelity data and build emulators to find Pareto-optimal designs. We apply our approach to a canonical problem on evaporator wick design and obtain fin-like topologies in the optimal microstructures which are also characteristics often observed in industrial applications.