The modelling and learning control of a phosphate drying furnace is considered. A mathematical model derived from mass and energy considerations is presented. This model consists of four hyperbolic partial differential equations. The numerical model simulation is performed using the method of characteristics, with the fuel flow and moisture content of the dried phosphate selected as control variables. Despite the external perturbations acting on the drying process, the main control objective is to minimize the fuel consumption and to keep the moisture content of the dried phosphate less than or equal to a certain value, provided that the temperature of the hot air, used as purging gas, equals or exceeds the saturation temperature. This control problem is modelled as the behaviour of a learning automaton in a random environment, subject to mean constraints. Using a reinforcement scheme, the automata update their action probabilities according to the response of the environment, and improve their behaviour with time. Detailed computer simulation results, which demonstrate the performance of this automaton controller, are presented.