Natrium super ionic conductor (NASICON) compounds form a rich and highly chemically tunable family of crystalline materials that are of widespread interest because they include exemplars with high ionic conductivity, low thermal expansion, and redox tunability. This makes them suitable candidates for applications ranging from solid-state batteries to nuclear waste storage materials. The key to an understanding of these properties, including the origins of effective cation transport and low, anisotropic (and sometimes negative) thermal expansion, lies in the lattice dynamics associated with specific details of the crystal structure. Here we closely examine the prototypical NASICON compound, NaZr2(PO4)3, and obtain detailed insights into such behavior via variable-temperature neutron diffraction and 23Na and 31P solid-state NMR studies, coupled with comprehensive density functional theory-based calculations of NMR parameters. Temperature-dependent NMR studies yield some surprising trends in the chemical shifts and the quadrupolar coupling constants that are not captured by computation unless the underlying vibrational modes of the crystal are explicitly taken into account. Furthermore, the trajectories of the sodium, zirconium, and oxygen atoms in our dynamical simulations show good qualitative agreement with the anisotropic thermal parameters obtained at higher temperatures by neutron diffraction. The work presented here widens the utility of NMR crystallography to include thermal effects as a unique probe of interesting lattice dynamics in functional materials.