  We show that the problem of computing the vacuum expectation values of gauge
invariant operators in the strong coupling limit of topologically massive gauge
theory is equivalent to the problem of computing similar operators in the
$G_k/G$ model where $k$ is the integer coefficient of the Chern-Simons term.
The $G_k/G$ model is a topological field theory and many correlators can be
computed analytically. We also show that the effective action for the Polyakov
loop operator and static modes of the gauge fields of the strongly coupled
theory at finite temperature is a perturbed, non-topological $G_k/G$ model. In
this model, we compute the one loop effective potential for the Polyakov loop
operators and explicitly construct the low-lying excited states. In the strong
coupling limit the theory is in a deconfined phase.
