The work deals with the development of a control system for heat exchangers with variable surface area of heat transfer, used, in particular, for heat pumps intended primarily for heat supply systems using the high-quality law of regulation of the heat supply mode (with a constant flow rate of the heat carrier). The aim of the work is to develop a scheme for the control of a heat exchanger with a variable surface area of heat exchange in which main disturbances will be compensated: i.e. the temperature of the heat carrier, heat carrier’s flowrates, and changes in the thermophysical parameters of the heat carriers. This goal has been achieved using a custom PID controller in the contour of control of the drive of the moving heat-insulating insert. To solve this problem, we obtained the equations of the statics of the heat exchanger with regard to the adjustable insert, the dynamic model of the heat exchanger taking into account this insert. The novelty of the work is control laws of an adjustable heat-conducting insert between the primary and secondary coolants of the heat exchanger, which allow compensating the main disturbances, which influence the heat exchanger. A method has been developed for solving differential-integral equations of heat exchanger statics with an insert (HEI), which allowed analytically expressing the ratio of average integral heat carrier temperatures in a heat exchanger depending on the heat exchanger length, which allows building a control system for a heat exchanger with a variable heat exchange surface area.