A HEAT exchanger has a multi-lumen tubing having one end connected to a supply fitting and another end connected to a return fitting. The tubing has a central lumen and a middle lumen that surrounds the central lumen and an outer lumen that surrounds the middle lumen. The supply fitting has an inlet and an outlet and a proximal port wherethrough an infusate is input to the HEAT exchanger. The supply fitting is configured such that its inlet is connected to the central lumen, its outlet connected to the outer lumen and its proximal port connected to the middle lumen of the tubing. The return fitting is configured to establish a through passage between the central lumen and the outer lumen of the tubing so that a heating fluid fed through the supply fitting to the central lumen is returned to the supply fitting by way of the outer lumen. The return fitting further has a distal port configured to connect to the central lumen of the tubing, so that the infusate fed to the proximal port of the supply fitting may be output from the distal port of the return fitting and after passing through the central lumen of the tubing. As the infusate traverses along the HEAT exchanger, it is heated by the heating fluid that flows along the central lumen and also by the rerouted heating fluid that flows along the outer lumen of the tubing. The HEAT exchanger is fluidly coupled to a heater by its inlet and outlet so that the temperature of the heating fluid for warming the infusate is maintained at a predetermined temperature.