Abstract: A mathematical model of temperature situations in the well is suggested based heat exchange principle. According to the model temperature of any depth and any time of drilling well can be calculated.Taking cold air as a circulation medium, a simplified calculation formula of the well temperature while drilling the formations with cold air is given. According to the formula temperature of any depth and any time of drilling the well with cold air can be calculated and representative dependence curves are given. Based the results of the calculating and considering, the temperature in annular space outside the drill stem should be no more than Ot,and corresponding suggestions are proposed.