  We analyse a $2+1$ dimensional model with charged, relativistic fermions
interacting through a four-Fermi term. Taking advantage of its large-$N$
renormalizability, the various phases of this model are studied at finite
temperature and beyond the leading order in $1/N$. Although the vacuum
expectation value (VEV) of a charged order parameter is zero at any non-zero
temperature, the model nevertheless exhibits a rich phase structure in the
strong coupling r\'egime, because of the non-vanishing VEV of a neutral order
parameter and due to the non-trivial dynamics of the vortex excitations on the
plane. These are: a confined-vortex phase which is superconducting at low
temperatures, an intermediate-temperature phase with deconfined vortices, and a
high-temperature phase, where the neutral order parameter vanishes. The
manifestation of superconductivity at low-temperatures and its disappearance
above a critical temperature is explicitly shown to be due to the vortex
confinement/deconfinement mechanism of Kosterlitz and Thouless. The ground
state does not break parity or time-reversal symmetries and the ratio of the
energy gap to $T_c$ is bigger than the conventional BCS value, for $N\ltwid
22$.
