Flux-pinned interfaces for spacecraft have been studied for almost a decade for their dynamic properties that allow designers to shape the dynamic behavior of spacecraft relative to one another. However, the efficacy of these interfaces hinges on the requirement that the type-II superconductors in the interface first be cooled below their critical temperature in the presence of a magnetic field, then held below their critical temperature for the duration of the dynamic interaction. Ground-based research often relies on consumable liquid nitrogen to cool the superconductors, but little work has been published on a flight-traceable cryocooler-based solution to meet the thermal constraints. This work provides estimates of the mass, power, and performance of a system to facilitate trade studies for potential spacecraft applications. This paper details a thermal system designed to cool three 16 mm thick, 56 mm diameter Yttrium Barium Copper Oxide disks to below their critical temperature of 88 K for a ground-based testbed. Data collected on the device shows that it successfully provides the thermal environment required for the flux-pinned interface while consuming 105 W of power. A thermal model accurately predicts heat flows and temperatures in the device. This model applied to a space environment predicts a power consumption of 67 W in a spaceflight device.