The Materials In Devices As Superconductors (MIDAS) spaceflight experiment is a NASA payload which launched in September 1996 on the Shuttle, and was transferred to the Mir Space Station for several months of operation. MIDAS was developed and built at NASA Langley Research Center (LaRC). The primary objective of the experiment was to determine the effects of microgravity and spaceflight on the electrical properties of high-temperature superconductive (HTS) materials. The thermal challenge on MIDAS was to maintain the superconductive specimens at or below 80 K for the entire operation of the experiment, including all ground testing and 90 days of spaceflight operation. Cooling was provided by a small tactical cryocooler. The superconductive specimens and the coldfinger of the cryocooler were mounted in a vacuum chamber, with vacuum levels maintained by an ion pump. The entire experiment was mounted for operation in a stowage locker inside Mir, with the only heat dissipation capability provided by a cooling fan exhausting to the habitable compartment. The thermal environment on Mir can potentially vary over the range 5 to 40°C; this was the range used in testing, and this wide range adds to the difficulty in managing the power dissipated from the experiment's active components.Many issues in the thermal design are discussed, including: thermal isolation methods for the cryogenic samples; design for cooling to cryogenic temperatures; cryogenic epoxy bonds; management of ambient temperature components' self-heating; and fan cooling of the enclosed locker. Results of the design are also considered, including the thermal gradients across the HTS samples and cryogenic thermal strap, electronics and thermal sensor cryogenic performance, and differences between ground and flight performance. Modeling was performed in both SINDA-85 and MSC/PATRAN (with direct geometry import from the CAD design tool Pro/Engineer). Advantages of both types of models are discussed. Correlation of several models to ground testing and flight data (where available) is presented. Both SINDA and PATRAN models predicted the actual thermal performance of the experiment well, even without post-flight correlation adjustments of the models.