  Charge and spin response in the planar $t-J$ model at finite temperatures are
investigated numerically, in the regime corresponding to cuprates at
intermediate doping. We show that the local spin correlation function is
$T$-independent, leading to $\chi''(\omega<J) \propto \tanh (\omega/2 T)$. The
current correlation function $C(\omega)$ appears to be $T$- as well as
$\omega$-independent, and the optical conductivity $\sigma \propto (1-
e^{-\omega/T})/\omega$. Such anomalous response functions are brought in
connection with the large entropy persisting at $T<J$.
