New organic aerogel using cellulose derivatives as precursors have promising insulating properties even at atmospheric pressure. In order to go further in the knowledge of their thermal behaviour, a relevant numerical model for estimating the phonon thermal conductivity of cellulose-based aerogels has been developed. The model accounts for the characteristic solid matrix at the local scale by using Kelvin cell representation of the porous structure. The cell size varies between 57 and 500 nm. The phonon heat transfer in the solid phase is treated by solving numerically the Boltzmann equation. The numerical results are confronted with previous analytical model and experimental measurements of the conductivity conducted on suitable aerogel samples.