Climate change enforces the implementation of sustainable industrial production with a special focus on pollution reduction, resource management, and energy savings. These goals are addressed by designing advanced control methods using the solution of an adequately formulated optimization problem. Heat exchangers represent particularly energy-demanding plants that are challenging from the advanced controller design point of view. Model predictive control (MPC) is a suitable control strategy to address the relevant control tasks. The complexity of the real-time implementation of MPC directly depends on the number of inequality constraints in the corresponding optimization problem. Therefore, the real-time computational effort can be reduced by removing inactive constraints. Since removing inactive constraints does not change the optimal solution, it is desirable to detect inactive constraints corresponding to the current system state measurement and remove them from the formulation of the MPC problem before running the optimization solver. However, external disturbances, parametric uncertainties, and setpoint changes often impact real plants, limiting the application range of the conventional constraint removal MPC approach. In this paper, we propose a modification of the conventional constraint removal approach to address this issue. The modified constraint removal approach achieves the robustness required for a practical application to a laboratory-scaled heat exchanger. The control performance of the heat exchanger is analyzed from the industrial perspective considering the computational time and energy consumption by implementing the control approach on a 32-bit microcontroller.