A heat exchanger delivers a pressurized dry gas stream cooled to an essentially constant temperature. The gas stream circulates in a coil with a functional part immersed in a liquid fraction of a second gas in a chamber of a corresponding container, whereby a portion of the wall of the container with the chamber contacts a liquid fraction of a third gas, providing a condensation surface for the second gas. The container containing the second pressurized gas is airtight. The condensation surface is dimensioned to allow absorption of a predetermined caloric power by the gas in the chamber without significant variation of temperature/pressure. Included is a monitored variable heater of the bath of the liquid fraction of the residual gas in the container, whereby total caloric power released by the circulating gas to be cooled and by the heater is constantly kept approximately equal to the specified caloric power.