A system for externally cooling a cask containing heat-emitting spent nuclear fuel includes the cask comprising a radiation shielding body defining an internal cavity configured to hold a canister containing the spent nuclear fuel. A continuously annular cooling jacket extends circumferentially around an external surface of the cask body. The cooling jacket may have a double shell construction including an internal cavity for a cooling medium which provides an external heat sink for absorbing heat radiated from the external wall surface of the cask generated by the spent nuclear fuel. The heat emitted by the spent nuclear fuel is absorbed by the cooling medium in the cooling jacket, thereby in turn cooling the cask. In one embodiment, the cooling medium may be dry ice which undergoes sublimation by absorbing the heat to change from solid to gaseous phase directly. The jacket may be formed of multiple segments.