The analysis of problems that make it difficult to obtain and solve a continuous model of a convective heat exchanger with cross-flowing streams performed in a paper. A method of transition to a continuous-discrete model proposed, that allows replacing the description of processes for heat carriers with cross-flowing to a description with parallel-flowing. The transition procedure carried out on the example of a coil surface cross-flow economizer and a direct-flow convective superheater of a drum boiler. The transfer functions of all input channels obtained using the discrete-continuous Laplace transform. Based on the calculations of frequency characteristics, conclusions on the possibility of using the model with parallel-flowing instead of the model with cross-flowing streams made