Classification of model media and its constitutive equations have been presented for thermo-mechanica coupling problem in the frame of constitutive theory, for thermal conduction, constitutive equations of a series of media, such as Gurtin material, Cattanco material, Fourier material and Jeffreys material, which belong to the frame. Deformation, Deformation gradient, temperature, temperature gradient, temperature rising rate, stresses, couple stresses and thermal flux are used which . The conception of thermal gradient material and its example are illuminated. And the simplified constitutive formula and the express theorem are given which harmonious are with no-othemess coordination.