The invention relates to a cryostat (20) for supercooled ( 4 K) stored in the second helium tank (5) in order to cool the supercooled liquid helium in the lower part (1) of the first helium tank (24). For this the Joule-Thomson cooling unit (2) either draws in liquid helium directly from the second helium tank (5), or the Joule-Thomson cooling unit (2) draws in liquid helium from the first helium tank (24), typically from an upper part (4) having liquid helium (> 4 K), and liquid helium can be transferred via the gas phase from the second helium tank (5) into the first helium tank (5). In this way the period of time in which the supercooled liquid helium of the first helium tank (24) can be cooled by means of a helium stock in the cryostat (20) can be arranged to be very long. The second helium tank (5) can be arranged at least partially adjacent to the first helium tank (24), in particular also around the first helium tank (24), in order to achieve a low overall height of the cryostat (20).