The present article deals with the boundary geometric control of a counter-current heat exchanger whose control is designed considering a model based on two partial derivative equations describing the variations of internal and external temperatures. The objective consists in controlling the internal fluid temperature, at the heat exchanger outlet, by manipulating the jacket temperature at its inlet boundary in spite of the variation of the temperature of the internal fluid at the heat exchanger inlet. The control law is designed considering the partial differential equation describing the temperature of the internal fluid, and the manipulated control is the boundary condition for the partial differential equation describing the temperature of the jacket fluid. The performances of the controller have been evaluated by simulation and the results show that it provides good regulation and tracking performances. The robustness of the controller has also been studied when velocities of both internal and external fluid, and physical properties of the heat exchanger are subjected to sudden fluctuations. For noisy measurements and for practical implementation, the moving average filtering and Kalman estimation approaches that provide the required state temperatures to be used in the controller are discussed. The control by manipulating the jacket flow rate has also been considered to compare the respective benefits of both strategies.