We argue that, at finite temperature, parity-invariant electrodynamics
with massive electrons in 2+1 dimensions can exist in both confined a
nd deconfined phases and has a confinement-deconfinement phase transit
ion of Berezinskii-Kosterlitz-Thouless type. We show that an order par
ameter for the confinement-deconfinement phase transition is a version
of the Polyakov loop operator whose average measures the free energy
of an external charge that is not an integral multiple of the electron
charge.