The invention relates to a system that includes: a insufflator (1) provided with a gas inlet (2), a valve (3) that regulates the flow to be supplied, an adjustable heater (4) for the gas to be supplied, a sensor (5) that detects the temperature of the heated gas, an outlet (6) for supplying the gas, and means (7) for propelling the gas toward the supply outlet (6); a disposable supply duct (8) that can be coupled to the gas outlet (6) for the insufflator (6) in order to convey the heated gas into the patient; and a return duct (9) for the gas, connected to a distal area of the supply duct (8) and to an inlet of the heater (4), wherein the gas supply duct (8) and the gas return duct (9) form a continuous recirculation circuit for heated gas.