Abstract This paper is concerned with the multivariable adaptive long-range predictive control of an epitaxy furnace which operates in batch manner. The epitaxy furnace is used for the fabrication of electronic devices. The thermal behaviour of the furnace is described by a set of three non-linear partial differential equations. The output vector is composed of the temperature in the heart of the furnace, in the tube, and in the heating elements. The heating powers are considered as control actions. A finite difference discretization scheme is used for the furnace model simulation. A CARIMA plant model is used to represent the dynamics of the considered furnace. The parameters of this model are estimated on-line using the constant trace recursive least squares method. The temperature-time evolution consists of three steps: a rising period, stabilization, and a falling period. So, we are interested in the tracking and regulation problem. Simulation results show that the furnace operates well under this adaptive control algorithm, which is easy to implement.