A superconducting device, such as a superconducting rotor for a generator or motor. A vacuum enclosure has an interior wall surrounding a cavity containing a vacuum. A superconductive coil is placed in the cavity. A generally-annularly-arranged, thermally-conductive sheet has an inward-facing surface contacting generally the entire outward-facing surface of the superconductive coil. A generally-annularly-arranged coolant tube contains a cryogenic fluid and contacts a generally-circumferential portion of the outward-facing surface of the sheet. A generally-annularly-arranged, thermally-insulative coil overwrap generally circumferentially surrounds the sheet. The coolant tube and the inward-facing surface of the coil overwrap together contact generally the entire outward-facing surface of the sheet.