Ice templated anisotropic foams based on cellulose nanocrystals (CNC) with densities ranging between 25 to 130 kg.m-3 were prepared from aqueous CNC dispersions. The thermal conductivities perpendicular to the columnar macropores direction increased in a non-monotonous way with the increasing CNC foam density while the thermal conductivity reached a minimum value for the CNC foam with the highest nanoporosity. Theoretical calculations including the solid and gas conduction within the foams as well as the thermal conductivity of water showed that phonon scattering at the solid-solid interfaces is responsible for reaching low thermal conductivity values. The foam wall nanoporosity, the particle alignment, the macropores orientation and the foam wall thickness seem to have a minimal effect on the thermal conductivity but can explain the deviations between the theoretical estimates and the experimental data. To this end the identification of the important influencing factors and the great importance of phonon scattering paves the way to design new fossil-free nanofibrillar foams with superinsulating properties.