The heat conduction equation in a coupled thermo-inelastic body. was derived by means of the irreversible thermodynamics and the measured data of the inner dissipation for metal. The coupled coefficients, which are dependent on temperature and inelastic strain rate, can be determined by the measured data of inner dis­sipation for metal. The functional of a coupled thermal inelastic problem was derived by means of non­linear functional analysis theory. Finally, it is proved that the critical points of the functional are the solu­tions of coupled thermal inelastic equations.