We developed flexible polymeric "heat-guiding materials" by simply drawing bacterial cellulose (BC) hydrogels to align the cellulose nanofibers and form "nanopapers" with anisotropic thermal conductivity. The in-plane anisotropy of thermal conductivity between the drawn and transverse directions increased as the draw ratio increased. For the drawn BC nanopapers, the coefficient of thermal expansion was found to be inversely correlated with the thermal diffusivity. We fabricated a planar spiral sheet by assembling the drawn BC strips to visualize the "heat flux controllability". The coexistence of heat-diffusing and heat-insulating capacities within the single nanopaper plane could help to cool future thin electronics.