The thermal characteristics of the helium circulation by a cryocooler are presented. This study is motivated mainly by our recent development of a closed-loop cooling system for Cyclotron K120 superconducting magnets without any replenishment of the cryogen. A channel is attached on the outer surface of the magnet form and the liquid helium passes through inside of the channel in order to cool the super conducting coils indirectly. A two-stage cryocooler as a heat sink is located at the top to recondense helium coming from the superconducting magnet form. The heat transfer in the natural circulation loop is discussed and the main dimensions of cooling system are determined.