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. From a thermal quadrupole formalism combined with the heat equation or the bio-heat equation when considering blood perfusion according to the branch level, a more compact model is used for system identification. The feasibility of online system identification is proposed for coefficient estimation by using an extended Prediction Error Method algorithm more suited for estimating fractional order systems: the Long Memory Prediction Error Method (LMRPEM).