  The thermodynamics of the spin-$S$ anisotropic quantum $XXZ$ chain with
arbitrary value of $S$ and unitary norm, in the high-temperature regime, is
reported. The single-ion anisotropy term and the interaction with an external
magnetic field in the $z$-direction are taken into account. We obtain, for
arbitrary value of $S$, the $\beta$-expansion of the Helmholtz free energy of
the model up to order $\beta^6$ and show that it actually depends on
$\frac{1}{S(S+1)}$. Its classical limit is obtained by simply taking $S\to
\infty$. At $h=0$ and D=0, our high temperature expansion of the classical
model coincides with Joyce's exact solution\cite{joyce_prl}. We study, in the
high temperature region, some thermodynamic quantities such as the specific
heat and the magnetic susceptibility as functions of spin and verify for which
values of $S$ those thermodynamic functions behave classically. Their finite
temperature behavior is inferred from interpolation of their high- and
low-temperature behavior, and shown to be in good agreement with numerical
results. The finite temperature behavior is shown for higher values of spin.
