  The finite-temperature optical conductivity $\sigma(\omega)$ in the planar
$t-J$ model is analysed using recently introduced numerical method based on the
Lanczos diagonalization of small systems (up to 20 sites), as well as by
analytical approaches, including the method of frequency moments and the
retraceable-path approximation. Results for a dynamical mobility of a single
hole at elevated temperatures $T>t$ reveal a Gaussian-like $\mu(\omega)$
spectra, however with a nonanalytical behavior at low $\omega$. In the single
hole response a difference between the ferromagnetic (J=0) and the
antiferromagnetic ($J>0$) polaron shows up at $T<J$. At larger dopings
numerical results in studied systems are consistent with the thermodynamical
behavior for $T>T^*\ge 0.1~t$. $\sigma(\omega)$ spectra show a non-Drude
falloff at large frequencies. In particular for `optimum' doping $n_h \sim 0.2$
we obtain in the low-$\omega,T$ regime the relaxation rate $\tau^{-1} \sim 0.6
(\omega+\xi T)$ with $\xi \sim 3$, being consistent with the marginal Fermi
liquid concept and experiments. Within the same regime we reproduce the nearly
linear variation of dc resistivity $\rho$ with $T$. This behavior is weakly
dependent on $J$, provided that $J<t$.
