Thermal contact conductance of metal-dielectric systems is a key parameter that has to be taken into account for the design and reliability of nanostructured microelectronic systems. This paper aims to predict this value for Si-Cu interfaces using molecular dynamics simulations. To achieve this goal, a modified embedded atom method interatomic potential for Si-Cu system has been set based upon previous MEAM potentials for pure Cu and pure Si. The Si-Cu cross potential is determined by fitting key properties of the alloy to results obtained by ab initio calculations. It has been further evaluated by comparing the structure and energies of Cu dimmers in bulk Si and CumSin clusters to ab initio calculations. The comparison between MD and ab initio calculation also concerns the energy barrier of Cu migration along the (110) channel in bulk Si. Using this interatomic potential, non equilibrium molecular dynamics has been performed to calculate the thermal contact conductance of a Si-Cu interface at different temperature level. The results obtained are in line with previous experimental results for different kind of interfaces. This confirms that the temperature variation of the thermal conductance might not find its origin in the electron-phonon interactions at the interface nor in the quantification of the energy of the vibration modes. The diffuse mismatch model is also used in order to discuss these results.