  In a 2+1-dimensional pure LGT at finite temperature the critical coupling for
the deconfinement transition scales as $\beta_c(n_t) = J_c n_t + a_1$, where
$n_t$ is the number of links in the ``time-like'' direction of the symmetric
lattice. We study the effective action for the Polyakov loop obtained by
neglecting the space-like plaquettes, and we are able to compute analytically
in this context the coefficient $a_1$ for any SU(N) gauge group; the value of
$J_c$ is instead obtained from the effective action by means of (improved) mean
field techniques. Both coefficients have already been calculated in the large N
limit in a previous paper. The results are in very good agreement with the
existing Monte Carlo simulations. This fact supports the conjecture that, in
the 2+1-dimensional theory, space-like plaquettes have little influence on the
dynamics of the Polyakov loops in the deconfined phase.
