  Within the t-J model we study several experimentally accessible properties of
the 2D-triangular lattice system Na$_x$CoO$_2$, using a numerically exact
canonical ensemble study of 12 to 18 site triangular toroidal clusters as well
as the icosahedron. Focusing on the doping regime of $x\sim0.7$, we study the
temperature dependent chemical potential, specific heat, magnetic
susceptibility and the dynamic Hall coefficient $R_H(T,\omega)$ as well as the
magnetic field dependent thermopower. We find a crossover between two phases
near $x \sim 0.75$ in susceptibility and field suppression of the thermopower
arising from strong correlations. An interesting connection is found between
the temperature dependence of the diamagnetic susceptibility and the
Hall-coefficient. We predict a large thermopower enhancement, arising from {\em
transport corrections} to the Heikes-Mott formula, in a model situation where
the sign of hopping is reversed from that applicable to Na$_x$CoO$_2$.
