Purpose: The present work is aimed to investigate the Deep Drawing process of Mg alloy sheet in Warm conditions, since through the temperature temperature the number of independent slip systems of the Mg alloys can be enlarged. Design/methodology/approach: A FE model and an equipment for warm deep drawing tests were created, since an experimental-numerical method was adopted; the most efficient heating positioning and the most suitable way of performing the WDD process was evaluated using data coming from the numerical model and temperature and punch load acquisition coming from experimental activity. Findings: Limit Drawing Ratio (LDR) equal to 2.6 for AZ31 Mg alloy (cross rolled, thickness 0.6mm) was obtained at the temperature 170oC using heater embedded in the female die; Drawing Ratio equal to 3.1 for the same Mg alloy (thickness 0.6mm) was obtained setting the temperature of the blank holder at 250oC (throughout heaters embedded in it) and cooling the central part using a water cooled punch. Research limitations/implications: Next step of the research will be to evaluate the optimal value of process parameters (speed, temperature and blank holder pressure) in order to draw the process window. Practical implications: The process with controlled heating and cooling technology can be applied in industrial production of a wide range of Mg alloy parts (structural components, covers for computer, communication and customer electronic, sportive equipments). Originality/value: Specific heating and cooling system were designed to analyse the influence of the different heating strategies combined with or without punch cooling on the WDD of AZ31 Mg alloy sheets.