Abstract: Conventional heat conduction analysis is based on continuous model, so it cannot describe heat transport between two bodies with contact. A numerical simulation method for heat conduction in discontinuous media is proposed, and a C++ computing code is developed. When simulating such problems, the domain is discretized as a series of blocks, and then each block is divided into several continuous elements. The boundaries of blocks are considered as potential contact interfaces, and the contact pairs are detected and marked efficiently according to the semi-spring & semi-edge combined contact model. In this method, a traditional continuous model is adopted for heat conduction inside each block (the Finite Volume Method is used in this paper), and a point-face type, edge-edge type heat conduction model is introduced for each contact interface. By modifying the stiffness factor of thermal conductivity for each contact interface, different heat transfer resistance effects can be realized. Numerical cases show that the method proposed in this paper can simulate heat conduction effects in discontinuous media well; the larger the stiffness factor on the contact interface, the smaller the heat conducting resistance effect of the contact interface; when the stiffness factor is larger than 100, interface resistance effects mostly disappear, and the results of discontinuous media and continuous media are more or less the same; finally, the interface stiffness factor only affects the transient process of heat conduction, but has no influence on steady state solution.