Metal rubber (MR) is a new-type damping material with special raw material and manufacturing process. The helix wire is considered as the geometric unit of MR. The thermal expansion model of the MR is established based on the thermal expansion analyses of micro-springs in different contact states with the Schapery model. Thermal experiments are conducted to analyze the effects of relative density and temperature on the thermal expansion property of metal rubber. The heat transfer process of the MR and the heat transfer model of helix wires are obtained based on MR microstructure. Under certain conditions, the heat transfer can be simplified into the single thermal conductions. Based on the Fourier law, thermal conduction of MR microstructure is analyzed using the thermoelectric analogy method. Combined with the equivalent coefficient law of the thermal conduction, the thermal conduction model of MR is established. The formula of the thermal conduction coefficient is derived. The accuracy of the theoretical model is verified by the experimental results. The theoretical and experimental results of the thermal expansion and heat transfer provide strong theoretical and calculative analytical foundation for the application of the MR in the heat insulation material field at high temperature.