The refrigeration power associated with the superconducting magnets and cryopumps of a steady-state fusion reactor is not negligible. The power has to be minimized because it plays a role in the power station global efficiency and in the required amplification factor Q. On the one hand, the long plasma discharges obtained in December 2003 on TORE SUPRA give an insight of the cryogenic losses that might be expected for a steady-state fusion reactor equipped with superconducting magnets. The superfluid bath of the windings in TORE SUPRA allows a simple calorimetric estimation of the cryogenic losses through the temperature evolution of the bath during the long discharge. The different kinds of losses in TORE SUPRA are estimated, discussed and explained. Not all of them will be present in a real reactor. On the other hand, in the framework of ITER preparation, the magnet system and the associated refrigerator have been dimensioned taking into account again all kinds of cold losses. This exercise is important because ITER, by its size, could be relevant to the steady-state reactor situation regarding refrigeration. Based on TORE SUPRA experiment and ITER design it is, therefore, possible to propose for the first time a preliminary figure for the cryoplant power of a steady-state reactor. The order of magnitude of the cryoplant power is ten times lower than that of the fusion reactor recycled power which can be considered acceptable.