An input output (I/O) linearizing control scheme for a gas-fired thermal cracking furnace is developed for a tubular reactor coil, which is a type of tubular reactor surrounded by gas-fired burners in the furnace. Due to the simultaneous interaction between the spatially distributed dynamics of the reactor coil and the lumped radiating wall, the typical proportional integral-derivative control widely used in industry may have insufficient performance to handle the complexity. In this work, a feedback I/O linearizing controller is applied to control a cracking furnace system that is described by a coupled PDE-ODE model: ethylene dichloride cracking. The cracked gas temperature is manipulated through the fuel gas flow to achieve the desired trajectories. Control performances of the developed controller are illustrated through simulation results for servo and regulatory problems. The proposed method provides more robustness to handle control problems without offset.