In this work, a model-based control of the melt temperature of a distributed parameter bi-zone model with moving interface of an extrusion process is studied. An energy-based controller is derived using internal energy as a storage function and controlled variable with the screw speed as control input. The stability of the controller is proved through the use of a Lyapunov-like candidate function. Finally, the practical usefulness of the method is illustrated by some closed-loop simulations of the experimentally verified model of the extrusion process. The interconnection of the moving interface is performed under the assumption of variable viscosity along the extruder and a finite-volume scheme is used for the discretisation of the dynamic model.