Abstract: A cryostat assembly (1) for a superconducting magnet assembly, with a helium tank (2) for liquid helium, whereby the superconducting magnet assembly (6) is located in the helium tank (2), with a nitrogen tank (3) for liquid nitrogen, whereby the nitrogen tank (3) encloses the helium tank (2), and with at least one access tube (4) in which the current lead is mounted through which current can be lead from the room-temperature warm area of the cryostat (1) into the superconducting magnet assembly (6), whereby the current lead assembly comprises at least one current lead with a normal conductor part (13) and a superconductor part (14) made of HTS material, characterized in that a terminal (12) of the at least one current lead, through which the normal conductor part (13) is electrically connected with the superconductor part (14) is thermally coupled with a wall of the nitrogen tank (3).