The formability of aluminium sheet can be improved by increasing the temperature in some parts of the sheet and cooling other parts. Simulation of this process requires an accurate material model for the yield function and the temperature and strain-rate dependent hardening. In simulations of cylindrical cup deep drawing, the quadratic Hill yield criterion results in too much thinning in the bottom of the cup. The Vegter yield function is more flexible and gives better predictions. The model for work hardening and the temperature and strain-rate sensitivity needs to be accurate over the complete temperature range between the cooled and the heated parts of the sheet. It is demonstrated that the Bergström model is able to model the flow stress of Al–Mg alloys up to 200 °C and medium strain rates. For higher temperatures and low strain rates the deviations with experiments increase.