The uniformity of temperature distribution on the surface of drawing punch has an important influence on the forming performance of cryogenic temperature drawn components. According to the first law of thermodynamics, a thermal conductivity model of the temperature field for punch was established, and the temperature field of punch during the cryogenic temperature cooling process was simulated by software Abaqus-6.14. Then, the accuracy of numerical simulation was verified by the cryogenic temperature cooling experiment. The results show that the temperature field of punch cavity during the cryogenic temperature cooling process presents a step-type uniform change. When the cooling time reaches 40 to 45 min, the temperature at deep hole 5 tends to be stable first, and the lowest experiment temperature is close to -121 ℃, which is 3.3% different from the simulated temperature of -125 ℃. When the cooling time reaches 50 to 55 min, the temperatures at deep hole 1 to deep hole 4 tends to be basically stable, and the lowest temperature reaches -176 ℃, which is only 5.1% different from the simulated lowest temperature of -185 ℃. At the same time, the heat flow density during the cooling process is inversely proportional to the thickness of punch cavity, while the heat conductivity is directly proportional to the thickness of punch cavity. The cooling time and liquid nitrogen consumption increase exponentially with the increasing of the thickness of  punch cavity. Thus, the research provides theoretical support for the solving of deep cooling temperature field of punch during the cryogenic temperature deep drawing process.