Realizing tunable functional materials with built-in nanoscale heat flow directionality represents a significant challenge that could advance thermal management strategies. Here we use spatiotemporally-resolved thermoreflectance to visualize lateral thermal transport anisotropy in self-assembled supercrystals of anisotropic Au nanocrystals. Correlative electron and thermoreflectance microscopy reveal that nano- to meso-scale heat predominantly flows along the long-axis of the anisotropic nanocrystals, and does so across grain boundaries and curved assemblies while voids disrupt heat flow. We finely control the anisotropy via the aspect ratio of constituent nanorods, and it exceeds the aspect ratio for nano-bipyramid supercrystals and certain nanorod arrangements. Finite element simulations and effective medium modeling rationalize the emergent anisotropic behavior in terms of a simple series resistance model, further providing a framework for estimating thermal anisotropy as a function of material and structural parameters. Self-assembly of colloidal nanocrystals promises an interesting route to direct heat flow in a wide range of applications that utilize this important class of materials.