We have used the generalized gradient approximation (GGA) to density functional theory to study the vibrational and thermal properties of guest-free Si136 and Ge136 clathrates. In order to study the effects of supercell size on our results, we have performed both 34 and 136 atom supercell calculations for each material. We find that the 34 atom supercell calculations predict a small frequency downshift (in comparison with the 136 atom supercell calculations) in the vibrational density of states of both materials. The GGA-predicted phonon frequency of Si136 (480 cm-1 at T=0 K) obtained from the 136 atom calculations is in very good agreement with the experimental value for Na1 Si136 (484 cm-1 at T=300 K). Using the results from our 136 atom calculations, we have also calculated the temperature dependence of the vibrational contributions to the Helmholtz free energy, the entropy, and the specific heat (CV) of the guest-free Si136 and Ge136 clathrates. The predicted and experimental heat capacities of Si136 are found to be in close agreement.