Uniaxial tensile test of a cross rolled magnesium alloy sheet was conducted under different temperatures and strain rates. The mechanical propriety of AZ31 magnesium alloy sheet was analyzed according to the true strain-stress curves. Then the non-thermal drawing process, during which the temperature of die, blankholder and blank is 200°C while the punch is kept at room temperature, was simulated by the thermo-mechanical coupled finite element method. The deformation behavior and the temperature change in the drawing process was investigated. Due to the heat conduction, there was non-uniform distribution of temperature along flange area, force transfer area and deformation area. Therefore the resistance of the force transfer area is enhanced and the warm formability of magnesium alloy sheet can be further improved. The thermo-mechanical coupled simulation provides a good guide for the development of non-isothermal drawing techniques.