Temperature dependent X-ray diffraction and Rietveld structure refinements on NaxSi136 clathrates with x = 1.1, 5.5, 12.6, 17.3, and 21.9 have been performed. Although the linear coefficient of thermal expansion (293 K < T < 423 K) of Si136 (x = 0) is only about 20% larger than that of the ground state a-Si (diamond structure), the linear coefficient of thermal expansion of NaxSi136 monotonically increases by more than 150% upon filling the framework cages with Na atoms in NaxSi136 (0 < x < 24), ranging from a = 2.6 × 10-6 K-1 (x = 0) to 6.5 × 10-6 K-1 (x = 24) by only varying the Na content, x. Taken together with heat capacity and bulk modulus data, the dramatic increase in thermal expansion can be attributed almost entirely to an increase in the mode-averaged Grüneisen parameter by a factor of more than 2 from x = 0 to x = 24, indicating the Na guests not only contribute low energy lattice vibrations in the phonon spectrum, but also significantly influence the character of the phonons as well. Due to the ability to fully vary the guest content, NaxSi136 (0 < x < 24) clathrates offer a useful model system to investigate the effects of the guest atoms on the lattice dynamics in clathrate materials. In particular, effects of the guest content can be experimentally discerned from the effects of differing framework or guest composition in studies of different clathrate compounds.