Abstract: A discontinuous Galerkin (DG) finite element method forthe discontinuous temperature field problems is presented. The DG methoduses discontinuous interpolation functions on the element boundaries, andthe discontinuous effect is considered by the penalty function techniques,in which the numerical flux and the stabilization term are adopted at theinterface. By substituting the numerical flux at the imperfect contactinterface with the definition of the thermal contact resistance, andeliminating the stabilization term, the present DG method can easily andaccurately capture the temperature jump caused by thermal contactresistance. Compared with the continuous Galerkin method, the present DGmethod also has higher computational efficiency in capturing the peak valueof the heat flux of the local high gradient temperature field. Numericalexamples also show that the present DG method is a novel numerical methodfor solving the coupling problems between the temperature and stress fieldcaused by thermal contact resistance.