A cooling system for indirectly cooled superconducting magnets of a superconducting winding, includes a winding form having canals formed therein through which liquid helium flows, the canals including a lower feed canal, an upper collecting canal and mutually parallel cooling canals interconnecting the feed and collecting canals in close thermal contact with the superconducting winding, a helium supply vessel disposed opposite to and elevated with respect to the winding form, the helium supply vessel having an outlet and a connecting stub, an outgoing line connected between the feed canal and the outlet, and a return line connected between the collecting canal and the connecting stub.