The preliminary results of experimental investigations of the thermal conductivity of nanocomposites built of amorphous silica nanoparticles embedded in the structure of crystalline methane are presented. The investigations were carried out on the samples containing the particles of linear dimensions of 5, 1020 and 42 nm. The measurements were performed with steady-state heat flow method in the temperature interval 2-35 K. A very simple thermal conductivity model shows that the dependence of the thermal conductivity coefficient of the investigated nanocomposites on temperature can be successfully described by taking into account only two mechanisms of the heat carrier dissipation: scattering of phonons by methane crystal grain boundaries and phonon-phonon interaction in U-processes. It was found that the low-temperature phonon mean free path is inversely proportional to the linear dimension of the nanopowder particles embedded in the methane crystal structure. (C) 2017 Elsevier Ltd. All rights reserved.