This article investigates the analytical time constants of temperatures transient response along a countercurrent heat exchanger when a mass flow-rate step change is applied on hot fluid flowing through the inner duct. The time constants of the hot and cold fluids are spatially linear and the fluid not submitted to step change shows two types of transient response. The first corresponds to a linear spatial decreasing of the time constant, while the second presents a uniform time constant along the heat exchanger. For each case, the analytical expressions of time constants are derived taking the conditions of the transient response on the boundaries of the heat exchanger. The condition which enables distinguishing the two cases is also proposed in this article. The comparison between theoretical and experimental results allows us to validate the analytical expressions, which depend on the initial and final steady states. The influence of the magnitude of flow-rate step change on the transient behavior is studied by maintaining the initial steady state. In the same way, the initial steady-state effect is investigated with the same magnitude of the flow-rate step change. The comparison of response time to positive and negative flow-rate step change is also presented for different values of cold-fluid flow rate.