The layered transition-metal oxide Nax CoO2 has been studied extensively both for its correlated electronic properties as well as for potential battery applications. It was discovered that high-temperature Na ion vacancy order and dynamics can be very useful to tailor low-temperature properties of members of this compound family. We have studied the Na-ion dynamics on the atomic length-scale in the Na-0.7 CoO2 compound by neutron spectroscopy. The temperature dependence of both the elastic and the inelastic intensities show steps at T-A approximate to 290K and T-B approximate to 400 K. At T-A the step is shown to be connected to low energy phonons, while at TB the Na ion diffusion suddenly gets fast enough, and the characteristic signal of quasielastic scattering appears. The current results further elucidate the subtle changes in the Na ion dynamics that have been revealed in our previous neutron diffraction studies [1], intimately connecting structural transformations at TA and TB with the opening-up of 1D and 2D Na-ion diffusion paths. Finally, the estimated diffusion coefficient above TB was found to differ from the one measured by muon- spin relaxation (mu(+) SR) [2] by about four orders of magnitude. However it might be that the present QENS data rather describe a fast localized prozess than a long range translational diffusion. Within this model the corresponding time scale (h/E) would be in the order of 50 ps.