The thermal conductivity of the CCl4 clathrate of 4-(3,4-dihydro-2,2,4-trimethyl-2H-1-benzopyran-4-yl)phenol (Dianin’s compound) has been measured using the steady-state potentiometric method. The temperature profile of the thermal conductivity coefficient of this crystalline material has glasslike character. The highly effective thermal resistance mechanism is ascribed to the scattering of acoustic phonons off localized low-frequency vibrations of the molecular moieties. The role and the behavior of the guest molecules in thermal conductivity are discussed in the wider context of the thermal properties of this material. The data presented complement the previous measurement on the clathrand and the ethanol clathrate of Dianin’s compound. In contrast with the latter, guest molecules in the CCl4 clathrate play a minor role in the thermal conductivity, as it is found to be much the same as the empty host lattice. The experimental results are interpreted on the premise of the resonant scattering model, with particular emphasis on the importance of the dynamics of the guest molecules to thermal resistance.