Temperatures transient response along a tubular counter flow heat exchanger is investigated when mass flow rate is subjected to sudden change. The dynamic behaviour is approximated by a first order response with a time constant. The hot fluid subjected to the flow rate step presents a decreasing linear time constant according to flow axis. The cold fluid, which is not submitted to the flow rate step, shows two types of transient response. The first one corresponds to a linear spatial increasing function of time constant while the second one presents a uniform time constant along the heat exchanger. Considering the conditions of the transient response on the boundaries of the heat exchanger, analytical expressions of time constants are obtained for each case, The comparison of the theoretical results with experimental data allows to validate the analytical expressions, which depend on initial and final steady-states. The influence of the flow rate step magnitude on transient behaviour is studied by maintaining the initial steady-state.