π-Stacking, which is a ubiquitous structural motif in assemblies of aromatic compounds, is well-known to provide a transport pathway for charge carriers and excitons, while its contribution to thermal transport is still unclear. Herein, based on detailed experimental observations of the thermal diffusivity, thermal conductivity, and specific heat of a single-crystalline triphenylene featuring a one-dimensionally π-stacked structure, we describe the nature of thermal transport through the π-stacked columns. We reveal that acoustic phonons are responsible for thermal transport through the π-stacked columns, which exhibit crystal-like behavior. Importantly, the thermal energy stored as intramolecular vibrations can also be transported by coupling to the acoustic phonons. In contrast, in the direction perpendicular to the π-stacked columns, an amorphous-like thermal transport behavior dominates. The present finding offers deep insight into nanoscale thermal transport in organic materials, where the constituent molecules exist as discrete entities linked together by weak intermolecular interactions.