A medium-scale reverse flow reactor for VOC combustion is investigated in the stationary and long-term transient states. Heat loss and dilution by fresh ail at the core of the reactor are accounted for. A simple linear dynamic model allows estimating temperature profiles at stationary state, and temperature dynamics in the transient state when VOC concentration varies. The extinction limit is also simply estimated. Heat loss and dilution are found to be a crucial phenomena and their effects on the characteristic time of the temperature response are established. Conversely, these phenomena do not seem to affect the extinction limit.