  We consider a lattice gauge theory at finite temperature in ($d$+1)
dimensions with the Wilson action and different couplings $\beta_t$ and
$\beta_s$ for timelike and spacelike plaquettes. By using the character
expansion and Schwinger-Dyson type equations we construct, order by order in
$\beta_s$, an effective action for the Polyakov loops which is exact to all
orders in $\beta_t$. As an example we construct the first non-trivial order in
$\beta_s$ for the (3+1) dimensional SU(2) model and use this effective action
to extract the deconfinement temperature of the model.
