A high temperature superconducting (HTS) magnet coil disposed within a cryostat is configured with a thermo-siphon cooling system containing a liquid cryogen. The cooling system is configured to indirectly conduction cool the HTS magnet coil by nucleate boiling of the liquid cryogen that is circulated by the thermo-siphon in a cooling tube attached to a heat exchanger bonded to the outside surface of the HTS magnet coil. A supply dewar is configured with a re-condenser cryocooler coldhead to recondense boiloff vapors generated during the nucleate boiling process.