The thermal Green's function method has been used to calculate the real part of the optical conductivity in the gauge-field model. The gauge invariant response functions were considered to the second order of the gauge field. We found that there is a structure in the frequecy range of a fraction of the Fermi energy. It is due to the excitation of particle-hole pair and a gauge field by a photon. In the small-frequency region, the optical conductivity is sensitive to temperature because' of boson excitations. In the intermediate and high frequency region it is not sensitive because fermion excitations dominates.