A cryostat system is kept at a cryogenic operating temperature without providing or supplying cryogenic fluids by a cryocooler. The cryostat system includes a superconducting magnet arrangement and a heat sink apparatus to prolong the time before the superconducting magnet arrangement quenches/returns to the normally conducting state if active cooling fails. The heat sink apparatus includes magnetocaloric material and is thermally connected to the superconducting magnet arrangement and/or to parts of the cryostat system through which ambient heat can flow to the superconducting magnet arrangement. In this way, the cryostat system can be operated in a truly “cryogen-free” manner while maintaining a sufficiently long time to quench in the event of potential operational malfunctions.