There is a growing requirement for high-field (>20 T) magnets capable of continuous operation, driven by the needs of both fundamental research and technological advance, particularly in application to an eventual pilot plant for magnetic confinement fusion. Even with HTS windings, such magnets will still require cryogenic cooling, and liquid helium (LHe) immersion, the typical solution to this problem, adds significantly to the operating expenses of such facilities. This reality makes cryogen-free cooling systems a necessity in future high-field magnet systems. The Princeton Plasma Physics Laboratory (PPPL) is exploring conduction-cooling systems of HTS pancake solenoids for a scanning tunneling microscopy (STM) facility at Princeton University, and potentially also for the central solenoid of the Fusion Nuclear Science Facility (FNSF). To these ends, PPPL is designing a cryostat to evaluate the thermal stability of a 5-6 T, 30 double-pancake (DP) REBCO insert coil of 40 mm ID / 70 mm OD, and smaller prototypes, operated in self-field with conduction cooling provided by a 2-stage GM cryocooler. The current design is expected to achieve 1st and 2nd stage temperatures of 44 K and 4-10 K, respectively, with the resistivity of DP-DP solder joints being the principal source of uncertainty in 2nd stage temperature predictions.