The modelling and optimisation of the thermal post-processing for bulk GaAs crystals is described, The annealing takes place in an approximately axisymmetric tube furnace and improves the crystal quality due to a more homogeneous distribution of defects and dopants. For this purpose the crystal has to be heated up to a certain temperature, as fast as possible for economical reasons. The crucial point is to minimise thermally induced stresses during heating. For this optimisation an algorithm based on a reduced order model (ROM) of the heating process is developed. By the aid of this model-predictive control (MPC) algorithm the required time to achieve the annealing temperature was decreased by 30% while the thermoelastic stress in the crystal is reduced by 10% compared to a standard procedure.