The unsteady state heat conduction of superconductors (Nb3Sn and V3Ga) was numerically studied. For this purpose, the non-linear successive over relaxation method has been applied. In this way, the boundary conditions of non-linear heat conduction, which contain thermophysical properties varying with temperature, are considered. The numerical results of the unsteady state heat conduction of these superconductors show different temperature distributions compared with normal heat conductors. According to the physical interpretation of heat conduction phenomena on a superconductor using the numerical analysis, the unsteady state temperature distributions are determined to the two solid media having different thermophysical properties in a lower transition temperature region and in a higher transition temperature region.