The deformation behaviour and the temperature change in cylindrical deep drawing of an aluminium alloy sheet at elevated temperatures are simulated by the combination of the rigid-plastic and the heat conduction finite element methods. The comparison with the experimental results shows that the forming limits and the necking sites are successfully predicted by the simulation. It is clarified that the appropriate distribution of flow stress depending on temperature must exist in the sheet for the higher limiting drawing ratio. The numerical as well as the experimental results show that the limiting drawing ratio in the warm deep drawing increases with the die profile radius.