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In this contribution, a theoretical study of the dynamic behaviour (open- and closed-loop) of a Feed-Effluent Heat Exchanger (FEHE) / Reactor system for the catalytic combustion of Volatile Organic Compounds (VOCs) is carried out. An additional supply of energy is provided by means of a furnace to achieve the desired reactor inlet temperature. The positive feedback of energy to the reactor inlet is a source of instability that leads to pronounced limit cycles in the main state variables. The strong thermal oscillations predicted can damage the catalyst and cause considerable stress on both the reactor and heat exchanger materials. To prevent this scenario, a control structure that considers the manipulation of a bypass flow of the feed stream around the FEHE is selected. A single-loop feedback control system is successfully applied to maintain the inlet temperature set-point, rejecting the VOC´s concentration disturbances and enabling a stable operation. The results demonstrate that the controllability of the process is ensured with high external heat supplies (low heat recovery in the FEHE) which increases the fuel demand and the operating costs. Additionally, a high FEHE transfer area enables efficient heat recovery and avoids the controllability loss due to a suitable by-pass valve regulation.