Scanning thermal microscopy is a powerful tool for investigating biological materials and structures like bamboo and its cell walls. Alongside nanoscale topographical information, the technique reveals local variations in thermal conductivity of this elegant natural material. We observe that at the tissue scale, fibre cells in the scattered vascular tissue would offer preferential pathways for heat transport due to their higher conductivities in both anatomical directions, in comparison to parenchymatic cells in ground tissue. In addition, the transverse orientation offers more resistance to heat flow. Furthermore, we observe each fibre cell to compose of up to ten layers, with alternating thick and thin lamellae in the secondary wall. Notably, we find the thin lamellae to have relatively lower conductivity than the thick lamellae in the fibre direction. This is due to the distinct orientation of cellulose microfibrils within the cell wall layers, and that cellulose microfibrils are highly anisotropic and have higher conductivity along their lengths. Microfibrils in the thick lamellae are oriented almost parallel to the fibre cell axis, while microfibrils in the thin lamellae are oriented almost perpendicular to the cell axis. Bamboo grasses have evolved to rapidly deposit this combination of thick and thin layers, like a polymer composite laminate or cross-laminated timber, for combination of axial and transverse stiffness and strength. However, this architecture is found to have interesting implications on thermal transport in bamboo, which is relevant for the application of engineered bamboo in buildings. We further conclude that scanning thermal microscopy may be a useful technique in plant science research, including for phenotyping studies.