A computational method is presented for obtaining the steady-state temperature responses of 1-2 pass heat exchangers subject to sinusoidal flow rate changes of large amplitude. The frequency- and amplitude- dependent describing functions between the input sinusoidal flow rate changes and the fundamental component of the steady-state response of the outlet temperature of tube-side or shell-side fluid are also derived. Numerical examples are given and it is shown that this method can reduce the computation time remarkably. Experiments are carried out: the steady-state responses to input sinusoidal flow rate changes are recorded for various values of amplitude. The experimental input-output relations of the fundamental components are determined from the recorded data using a Fourier analysis technique on a digital computer, and the experimental data are shown to be in good agreement with the theoretical results obtained by the present describing functions.