Additive manufacturing is now a promising option to obtain porous customized structures at relatively low scales. The capability to design structures with tunable heat transfer performance compared to conventional porous materials, such as open-cell foams, is very interesting to the user. In this study, we investigated heat conduction in a drilled-hollow-sphere architected foam, inspired by Triply-Periodic Minimal Surfaces (TPMS) and foam structures, generated using perforated spherical hollow shells connected with cylindrical binders. Temperature fields and heat fluxes in the foam were predicted numerically, and the effective thermal conductivity of the foam was calculated for different sets of the binder angle, the shell thickness, and the perforation radius. The dependence of the foam porosity on the binder angle and perforation radius was also pointed out. Predictions were validated by comparing them with data available from the literature. Results showed that varying the characteristics of the investigated drilled-hollow-sphere architected foam, its predicted effective thermal conductivity can be adjusted by more than one order of magnitude larger or smaller than that of conventional foams, making architected foams promising enhancers of their heat transfer performance. Finally, new dimensionless correlations among the effective thermal conductivity and some significant morphological parameters of the foam were derived and presented for practical use.