  Lattice Yang-Mills theories at finite temperature can be mapped onto
effective 3d spin systems, thus facilitating their numerical investigation.
Using strong-coupling expansions we derive effective actions for Polyakov loops
in the $SU(2)$ and $SU(3)$ cases and investigate the effect of higher order
corrections. Once a formulation is obtained which allows for Monte Carlo
analysis, the nature of the phase transition in both classes of models is
investigated numerically, and the results are then used to predict -- with an
accuracy within a few percent -- the deconfinement point in the original 4d
Yang-Mills pure gauge theories, for a series of values of $N_\tau$ at once.
