Described is a method of making an apparatus for oxygenating and controlling the temperature of blood in an extracorporeal circuit, the steps comprising: providing a core through which blood can be supplied to the apparatus from a patient; providing a heat exchanger about the core such that blood from the core can move radially outward through the heat exchanger; providing an oxygenator about the heat exchanger such that blood from the heat exchanger can move radially outward through the oxygenator; and placing the core, heat exchanger and oxygenator in a housing that includes an inlet in communication with the core and an outlet that is located radially outward from the inlet in order to define a flowpath for blood through the apparatus.