A portable, foldable, soft-sided insulated container has an a lid mounted carrier, or seat, for a substantially rigid container of a thermal storage medium, such as water. The container assembly may be free of any rigid tub, and may thus retain the ability to fold. The carrier is a substantially rigid plate or panel, or array, that mounts to an otherwise soft panel. The panel, or portion of a panel, to which the rigid carrier mounts is a panel that may tend to stay substantially flat (or curved) when the container assembly is folded. The mounting is such that the substantially rigid thermal storage medium container can slide in and out of the seat. When not in use the entire assembly can be folded into a collapsed position for storage.