A computational method is introduced which allows to determine the time-dependent temperature distribution in dust deposits on heated surfaces or in a heated environment. The method may consider any kind of boundary conditions (given temperature, given heat flux or given heat transfer conditions). The suitability of the method is proved agaist a number of experimental results. Furthermore the critical conditions (critical heat flux, critical thickness of the layer) for the ignition of a coal dust on a hot surface with constant heat flux are predicted.