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A compact cryogenic cooling system is developed for small HTS magnets to be continuously refrigerated in subcooled liquid nitrogen at temperatures below 77 K by a cryocooler. This thermal design is particularly useful when electrical insulation and compactness are significant at the same time. HTS elements are immersed in a cylindrical liquid-nitrogen vessel, and a copper band is brazed around the exterior sidewall of the cylinder at vertical location just under the liquid level in order to achieve peripherally uniform cooling with a GM cryocooler. The vapor space above liquid nitrogen in the vessel provides a fully open room for current leads and mechanical supports to the magnets. Heat is removed from the HTS magnets by natural convection of subcooled liquid nitrogen to the cold sidewall. The key components are designed based on heat transfer analysis. A prototype is fabricated, and it is successfully demonstrated that the thermal load is effectively removed and temperature is spatially uniform.