The thermal conductivity of crystalline methane samples with spherical palladium nanoparticles of diameter 6, 8, 10, 12, 18 and 24 nm embedded in the CH4 structure was determined in the temperature range 2–35 K. The spherical nanoparticles featured a low dispersion of the sphere diameter and the volume fraction of the nanoparticles in the nanocomposites amounted to 0.15. Time relaxation approximation analysis shows that the matrix resistive phonon scattering processes are dominated by diffuse scattering of phonons by matrix-nanoparticle boundaries. Other considered intensities of resistive scattering mechanisms of phonons, i.e., scattering by point defects, by dislocation strain fields and by phonons in U-processes remain almost the same in nanocomposites and pure methane crystal. In transfer of the heat through the investigated nanocomposites non-resistive scattering of phonons by the nanoparticles, such as phonon specular scattering and multiple scattering of phonons show very high intensity. The nanocomposites formed of 18 and 24 nm nanospheres show anomalous power increase of the thermal conductivity coefficient dependence on temperature, exceeding the values known for a typical dielectric crystal.