Abstract: The invention relates to heating engineering. The inventive method for heating or cooling fluid medium consists in supplying a cooled or heated fluid medium in a through channel and in subsequently heating or cooling said fluid medium therein at least in two stages. Said through channel is divided into heating and cooling stages having the same length. The temperature of each stage increases in the case of heating and reduces in the case of cooling stepwisely and directly proportionally in a direction away from the thirst stage to the next stage. The heated or cooled water is supplied to the through channel tangentially at an angle of 45–90° to the generatrix of the internal surface thereof at a point where the fluid medium is introduced. Said invention increases the efficiency of the process of heating or cooling said fluid medium.