Abstract: The invention concerns a cooling/warming jacket pad for the containment of physiological organs such as hearts and kidneys during medical procedures. The pad when unused is a substantially flat, slim pad having an interior compartment in the form of a passage such that cooling fluid flows past substantially all interior surfaces and null patches of flow are at least mitigated. The pad has an inlet tube and an outlet tube preferably located to minimize interference with a surgeon or surgeons. Portions of the pad may be wrapped over each other to form a cone-shaped jacket within which the organ is contained. The pad may be shaped so that the narrow end of the jacket is open so that physiological tissues and tubes, e.g. blood vessels may project therethrough for connection to like tissues and tubes of a patient while the organ is still within the jacket. To provide this opening the flat pad may have a bay between the wrap-over portions.