  We establish a close relation between the spatial string tension of the
(3+1)-dimensional $SU(3)$ gauge theory at finite temperature ($\sigma_s$) and
the string tension of the 3-dimensional $SU(3)$ gauge theory ($\sigma_3$) which
is similar to what has been found previously for $SU(2)$. We obtain
$\sqrt{\sigma_3} = (0.554 \pm 0.004) g_3^2$ and $\sqrt{\sigma_s} = (0.586 \pm
0.045)g^2(T) T$, respectively. For temperatures larger than twice the critical
temperature results are consistent with a temperature dependent coupling
running according to the two-loop $\beta$-function with $\Lambda_T =
0.118(36)T_c$.
