The thermal conductive properties, including the thermal diffusivity and resultant thermal conductivity, of nonwoven nanocellulose sheets were investigated by separately measuring the thermal diffusivity of the sheets in the in-plane and thickness directions with a periodic heating method. The cross-sectional area (or width) of the cellulose crystallites was the main determinant of the thermal conductive properties. Thus, the results strongly indicate that there is a crystallite size effect on phonon conduction within the nanocellulose sheets. The results also indicated that there is a large interfacial thermal resistance between the nanocellulose surfaces. The phonon propagation velocity (i.e., the sound velocity) within the nanocellulose sheets was estimated to be similar to 800 m/s based on the relationship between the thermal diffusivities and crystallite widths. The resulting in-plane thermal conductivity of the tunicate nanocellulose sheet was calculated to be similar to 2.5 W/mK, markedly higher than other plastic films available for flexible electronic devices.