The thermal conductivity λ of normal and deuterated tetrahydrofuran (THF) clathrate hydrates has been measured at temperatures in the range 55-250 K and at pressures up to 0.16 GPa. The normal and deuterated samples exhibited the same values of λ to within 5%. At isobaric heating, the transition from the proton ordered low temperature (LT) phase to the proton disordered high temperature (HT) phase was detected as a discontinuous decrease of λ by about 15% for both the normal and the deuterated samples. The magnitude is nearly the same as that found previously for the related transition phase XI → phase Ih of ice and might be due to a change in the lattice anharmonicity. The thermal conductivity of the LT and HT phases increased slightly with increasing temperature and, hence, these crystalline phases exhibited both a glass-like λ(T). These results can be described using the resonance scattering model in which the phonons are scattered against THF vibrations. The LT phase of both samples exhibited a slight increase of λ with increasing pressure whereas that of the HT phases was roughly independent of pressure, showing that λ does not depend on density.