  All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain
$H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + \Delta
S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies
$\Delta=0 , \cos(0.3\pi)$, and 1. The dynamic spin pair correlations $<
S_{l+n}^{\mu}(t) S_l^{\mu} > , (\mu=x,z)$, the dynamic structure factors
$S^{\mu}(q,\omega)$, and the intermediate structure factors $I^{\mu}(q,t)$ are
calculated for arbitrary temperature T. It is found, that for all T,
$S^{z}(q,\omega)$ is mainly concentrated on the region $|\omega| <
\varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the
two-spinon continuum, although excited states corresponding to a much broader
frequency spectrum contribute. This is also true for the Haldane-Shastry model
and the frustrated Heisenberg model. The intermediate structure factors
$I^{\mu}(q,t)$ for $\Delta \neq 0$ show exponential decay for high T and large
q. Within the accessible time range, the time-dependent spin correlation
functions do not display the long-time signatures of spin diffusion.
