  For the free Fermion gas at thermodynamic equilibrium, the temperature which
represents the averaged kinetic energy is demonstrated to have the proper
property which is invariant under the Lorentz boost, using the conceptions of
the relativistic quantum field theory and statistical physics. The
thermodynamic interaction is described by the coupling of particles with the
vacuum of a scalar pseudo boson which features a self-interaction. The various
measurement of the apparent temperature of a moving body is also investigated.
