We present the results of measurements of the dc-magnetic susceptibility chi(T) and the Na-23-NMR response of Na0.70CoO2 at temperatures between 50 and 340 K. The chi(T) data suggest that for T>75 K, the Co ions adopt an effective configuration of Co3.4+. The Na-23-NMR response reveals pronounced anomalies near 250 and 295 K, but no evidence for magnetic phase transitions is found in chi(T). Our data suggest the onset of a dramatic change in the Co 3d-electron spin dynamics at 295 K. This process is completed at 230 K. Our results may be interpreted as evidence for either a tendency to electron localization or an unconventional charge-density-wave phenomenon within the Co 3d electron system near room temperature.