In cardiac surgery where extracorporeal circulation is used, the lungs are temporarily disconnected from the body and are connected to a device that provides air and blood. To minimize the risk of tissue damage, the lungs are subjected to mild hypothermia. Heat transfer modeling offers the potential to enhance temperature regulation through a more advanced approach. A thermal model, based on a thermal quadrupoles, also called two-port network, offers a wide frequency range applicability, making it suitable for modeling the human breathing. This modeling approach can also be adapted to incorporate the influence of blood flow, which also serves as a natural temperature regulator in the human body. This is accomplished by combining the thermal two-port network with the bio-heat equation. The main contributions are in the analytical expressions of the thermal impedances and by proposing a Butterworth approximation model for the equivalent impedances of lung thermal transfers.