The present work is focused on the investigation of the role of temperature and punch speed in warm deep drawing of AZ31 magnesium alloy. To this purpose, an experimental campaign, defined using a proper DOE approach, has been performed. The experimental results, in terms of the Limiting Drawing Ratio, have shown that drawability is strongly affected by the process parameters. In particular, Limiting Drawing Ratio exhibits the peak value at 250°C. As far as the effect of punch speed is concerned, it depends on temperature: at 200°C drawability increases with decreasing punch speed whilst a reverse behaviour is observed at 250 and 300°C. The experimental results have been analysed by ANOVA in order to evaluate the effect of the single independent factors and their interactions on the dependent one.