In this review, we summarize the recent progress in thermal conductivity analysis of nanocellulose materials called cellulose nanopapers, and compare them with polymeric materials, including neat polymers, composites, and traditional paper. It is important to individually measure the in-plane and through-plane heat-conducting properties of two-dimensional planar materials, so steady-state and non-equilibrium methods, in particular the laser spot periodic heating radiation thermometry method, are reviewed. The structural dependency of cellulose nanopaper on thermal conduction is described in terms of the crystallite size effect, fibre orientation, and interfacial thermal resistance between fibres and small pores. The novel applications of cellulose as thermally conductive transparent materials and thermal-guiding materials are also discussed.