Topological Invariance at Finite Temperature

We examine the thermal behavior of a theory with charged massive vector matter coupled to Chern-Simons gauge field. We obtain a critical temperature Tc, at which the effective mass of vector field vanishes, and the system transfers from a symmetry broken phase to topological phase. The phase transition is suggested to be of the zeroth order, as the free energy of the system is discontinuous at Tc. Application to the (2+1) dimensional quantum gravity is briefly discussed.