Superconducting multipole magnets (wigglers, undulators) are a powerful tool for creating powerful sources of a synchrotron radiation with high brightness. Such devices operating in conditions of restricted access, must have high reliability in continuous operation for a long time. The cryogenic system should have continuous temperature control of the main parts of a cryostat and a magnet to keep reliability the system. Bath cryostats with magnets in liquid helium with use of cryocoolers are sufficiently well developed and have high reliability. The report presents the design of a cryostat with use of cryocoolers, which provides for indirect cooling of a magnet without direct contact with liquid helium, and the magnet is located in the insulating vacuum. Primary cooling is done using heat tubes filled with nitrogen. Maintaining low temperatures of the magnet is provided by a heat tube filled with helium in a siphon mode. Prototype of such a cryostat has demonstrated high reliability and efficiency in the APS (Advanced Photon Source, USA) superconducting undulator and superconducting wiggler ANKA-CLIC (Germany).