In this study the authors minimise the total process cost for the heating of solid particles in a horizontal fluidised bed by an optimal choice of the inlet heating gas temperature profile and the total gas flow. Solid particles flowed along the apparatus and were heated by a hot gas entering from the bottom of the fluidised apparatus. The hydrodynamics of the fluidised bed is described by a two-phase Kunii - Levenspiel model. We assumed that the gas was flowing only vertically, whereas solid particles were flowing horizontally and because of dispersion they could be additionally mixed up in the same direction. The mixing rate was described by the axial dispersion coefficient. As any economic values of variables describing analysing process are subject to local and time fluctuations, the accepted objective function describes the total cost of the process expressed in exergy units. The continuous optimisation algorithm of the Maximum Principle was used for calculations. A mathematical model of the process, including boundary conditions in a form convenient for optimisation, was derived and presented. The optimization results are presented as an optimal profile of inlet gas temperature. The influence of heat transfer kinetics and dispersion coefficients on optimal runs of the heating process is discussed. Results of this discussion constitute a novelty in comparison to information presented in current literature.