  The Green-Kubo relation and fluctuation-dissipation theorem are employed to
calculate the shear viscosity $\eta$ of a finite hot nucleus directly from the
width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio
$\eta/s$ of shear viscosity $\eta$ to entropy density $s$ is extracted from the
experimental systematics of the GDR in copper, tin and lead isotopes at finite
temperature $T$. These empirical results are then compared with the predictions
by several independent models, as well as with almost model-independent
estimations. Based on these results, it is concluded that the ratio $\eta/s$ in
medium and heavy nuclei decreases with increasing temperature $T$ to reach
$(1.3 - 4)\times\hbar/(4\pi k_{B})$ at $T=$ 5 MeV.
