Abstract—The article addresses matters concerned with developing the linear theory of constructing multipoint models intended for synthesizing automatic closed loop control systems of thermal power facilities. The multipoint approximation models are oriented at solving practical problems to an extent greater than the models with distributed parameters. The transfer functions of multipoint linear models can be obtained using the signal graph method; however, this method is not always suitable for being used without additional simplifications, in particular, the assumption about “independent heating.” In this study, for obtaining the dynamic characteristics of countercurrent heat exchangers involving longitudinal motion of coolants, it is proposed to use the discretecontinuous Laplace transform method. The method is developed taking the boiler economizer as an example. The article shows the way in which a shift can be made to the process circuit with longitudinal countercurrent motion by using the method of decomposing the economizer surface with cross flow of coolants into segments. Analytical expressions for the model’s transfer functions of an arbitrary order are obtained. Complex frequency responses for eight economizer channels are calculated. The characteristics of multipoint models and models with distributed parameters only for water and for both coolants are compared with each other. Recommendations for selecting the minimally admissible order depending on the input disturbance kind are given. The possibility of using a model with lumped parameters for the external coolant is revealed. It is shown that simplification of the external coolant model down to the first order has hardly any effect on the characteristics of only the internal coolant’s two temperature channels connected with its own input actions in terms of flowrate and temperature.