Provided is an assembly for insulating substantially vertical runs of cooled surfaces that are continuously or periodically exposed to air or another gas that has a dewpoint temperature above that of the cooled surface, thereby resulting in condensation water vapor on or adjacent the cooled surface. One embodiment of the insulating assembly provides a wicking material layer adjacent the cooled surface that, in combination with transporting and evaporating structures, removes the condensate from the vicinity of the cooled surface and allows for its evaporation into the ambient gas surrounding the exterior surface of the insulating assembly. Another embodiment provides for exposing the condensate to an internal conditioned gas stream to provide for evaporation that does not necessarily utilize an exterior surface. Both embodiments remove condensate from the insulating structure and thereby tend to avoid any substantial condensate accumulation and maintain the insulating performance.