  It is known that in the 2+1 dimensional quantum electrodynamics with
Chern-Simons term, spontaneous magnetic field induces Lorentz symmetry
breaking. In this paper, thermodynamical characters, especially the phase
structure of this model are discussed. To see the behavior of the spontaneous
magnetic field at finite temperature, the effective potential in the finite
temperature system is calculated within the weak field approximation and in the
fermion massless limit. We found that the spontaneous magnetic field never
vanishes at any finite temperature. This result doesn't change even when the
chemical potential is introduced. We also investigate the consistency condition
and the probability that fermion stays in a lowest Landau level at finite
temperature.
