Semiconductor device assemblies are provided with a package substrate including one or more layers of thermally conductive material configured to conduct heat generated by one or more of semiconductor dies of the assemblies laterally outward towards an outer edge of the assembly. The layer of thermally conductive material can comprise one or more allotropes of carbon, such as diamond, graphene, graphite, carbon nanotubes, or a combination thereof. The layer of thermally conductive material can be provided via deposition (e.g., sputtering, PVD, CVD, or ALD), via adhering a film comprising the layer of thermally conductive material to an outer surface of the package substrate, or via embedding a film comprising the layer of thermally conductive material to within the package substrate.