  The spin dynamics at the finite temperature for the t-J model in the
underdoped and optimal doped regimes is studied within the fermion-spin theory.
It is shown that the dynamical spin structure factor spectrum at the
antiferromagnetic wave vector $Q=(\pi,\pi)$ are separated as low- and
high-frequency parts, respectively, but the high-frequency part is suppressed
in the dynamical susceptibility spectrum $\chi^{''}(Q,\omega)$, while the
low-frequency part is the temperature dependent, which are in qualitative
agreement with the experiments and numerical simulations.
