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New technologies are emerging which allow us to manipulate and assemble 2-dimensional (2D) building blocks, such as graphene, into synthetic van der Waals (vdW) solids. Assembly of such vdW solids has enabled novel electronic devices and could lead to control over anisotropic thermal properties through tuning of inter-layer coupling and phonon scattering. Here we report the systematic control of heat flow in graphene-based vdW solids assembled in a layer-by-layer (LBL) fashion. In-plane thermal measurements (between 100 K and 400 K) reveal substrate and grain boundary scattering limit thermal transport in vdW solids composed of one to four transferred layers of graphene grown by chemical vapor deposition (CVD). Such films have room temperature in-plane thermal conductivity of ~400 Wm⁻¹ K⁻¹. Cross-plane thermal conductance approaches 15 MWm⁻² K⁻¹for graphene-based vdW solids composed of seven layers of graphene films grown by CVD, likely limited by rotational mismatch between layers and trapped particulates remnant from graphene transfer processes. Our results provide fundamental insight into the in-plane and cross-plane heat carrying properties of substrate-supported synthetic vdW solids, with important implications for emerging devices made from artificially stacked 2D materials.