Transport and heat exchange phenomena occuring in a heat exchanger can be modeled as first-order hyperbolic partial differential equations (PDEs). Reformulating these equations as a time-delay system preserves the infinite-dimensional property of the system, yet decreases its mathematical complexity. Using a space-averaging technique and the method of characteristics, this paper proposes a time-delay system modeling of the flow temperatures of a heat exchanger. We propose to use a gradient-descent optimization method to estimate the parameters of this time-delay system, using boudary measurements of temperature in the heat exchanger. The interest of this approach is emphasized with experimental data obtained from the test-bench.