Thermal Energy Storage (TES) systems represent a cornerstone in the development of sustainable energy solutions, enhancing the flexibility in energy management. Heat exchangers are pivotal components of TES systems and they require precise control to optimize efficiency. Proportional-Integral-Derivative (PID) controllers are commonly employed for heat exchangers control but, since these systems are subject to time-delays and nonlinearities, their performance leaves room for enhancement. This paper explores the potential of Proportional-Integral-Derivative-Acceleration (PIDA) control, also known as PIDD or PIDD², that introduces a double derivative (acceleration) component to the traditional PID structure. The capability of PIDA control in improving system performance compared to conventional PID controllers is evaluated through a simulation study performed on a realistic heat exchanger simulator. The obtained results show the efficacy of PIDA control in enhancing control performance without adding additional complexity or tuning efforts.