In a superconducting magnet apparatus, at least one superconducting winding and an outer vacuum chamber are provided. A thermal radiation shield is located between the superconducting winding and the outer vacuum chamber. A cryogen vessel is positioned within the thermal radiation shield and within the outer vacuum chamber. The superconducting winding is positioned outside of the cryogen vessel. A refrigerator is operable to cool the cryogen vessel to a liquid cryogen temperature and to cool the at least one thermal radiation shield to an intermediate temperature between the liquid cryogen temperature and a temperature of the outer vacuum chamber. A substantial portion of an outer surface of the cryogen vessel has a thermal emissivity at the liquid cryogen temperature which is greater than an average surface emissivity of the superconducting winding by at least 0.1.