A heat exchange system includes cooling tubes that carry coolant and are placed on an external surface of a storage tank, which may be spherical, cylindrical, or other shape. The storage tank may be a cryogenic rocket fuel tank. The cooling tubes are bent to particular radius of curvatures that correspond to the varying curvatures of the storage tank. A network of spacers and bridge brackets with adjustable setscrews are used to precisely place the cooling tubes in correct positions on the external surface of the storage tank. Once placed in the desired position, the setscrews are adjusted to maximize the surface area contact between the cooling tubes and the exterior surface of the storage tank, resulting in optimal heat transfer without overstressing the materials of the tubing or the storage tank. The precisely positioned tubes may then be permanently affixed to the exterior surface of the storage tank using a cryogenic adhesive.