Under certain conditions (steady flows, no temperature dependence of thermophysical properties), the temperature rise at any point (solid or fluid) of a heat exchanger, whatever its type, is a convolution product between the thermalsource and the corresponding transfer function.Here a counter-flow heat exchanger is considered, where the hot fluid inlet temperature varies with time while the cold fluid inlet temperature is kept equal to the initial uniform temperature in the whole system. The transfer functions are estimated using synthetic temperature responses. This shows that temperature sensors located on the external surface of the exchanger can be used to detect fouling or to give informations about the outlet bulk temperatures of the fluids (steady state or transient thermal regimes).