Layering two-dimensional van der Waals materials provides a high degree of control over atomic placement, which could enable tailoring of vibrational spectra and heat flow at the sub-nanometer scale. Here, using spatially resolved ultrafast thermoreflectance and spectroscopy, we uncover the design rules governing cross-plane heat transport in superlattices assembled from monolayers of graphene (G) and MoS₂ (M). Using a combinatorial experimental approach, we probe nine different stacking sequences, G, GG, MG, GGG, GMG, GGMG, GMGG, GMMG, and GMGMG, and identify the effects of vibrational mismatch, interlayer adhesion, and junction asymmetry on thermal transport. Pure G sequences display evidence of quasi-ballistic transport, whereas adding even a single M layer strongly disrupts heat conduction. The experimental data are described well by molecular dynamics simulations, which include thermal expansion, accounting for the effect of finite temperature on the interlayer spacing. The simulations show that an increase of ∼2.4% in the layer separation of GMGMG, relative to its value at 300 K, can lead to a doubling of the thermal resistance. Using these design rules, we experimentally demonstrate a five-layer GMGMG superlattice "thermal metamaterial" with an ultralow effective cross-plane thermal conductivity comparable to that of air.