Discotic columnar liquid crystals (LCs) hold promise as thermal interface materials that allow heat to flow preferentially in the desired direction, whereas their heat transport properties remain elusive, particularly in terms of anisotropy related to their columnar alignments. Using a discotic columnar LC (TPC4F6) that allows for complete alignment control by applying mechanical shear, we investigated the alignment dependence of the thermal diffusivity using a dedicated setup for micro temperature wave analysis. We found that the thermal diffusivity in the direction perpendicular to the columns is larger, compared with the direction along the columns. Interestingly, this trend is opposite to that observed for a single crystal system composed of an identical aromatic core motif. This result demonstrates that the anisotropy of heat transport can change depending on the phases of materials even when they have similar compositions, providing insights into the design of organic materials for thermal management.