The intermittent flow cold storage heat exchanger is one of the most important components of the pulse tube expansion refrigerator based on the reverse Brayton cycle. In the experimental system, the volume and heat transfer of the helical tube play a decisive role in the stable operation of the whole experimental system. However, there are few studies on heat transfer in a helical tube under helium working medium and intermittent flow conditions. In this paper, a process and method for calculating the volume of a helical tube are proposed based on the gas vessel dynamics model. Subsequently, a three-dimensional simulation model of the helical tube was established to analyze the heat transfer process of cryogenic helium within the tube. The simulations revealed that the temperature of helium in the tube decreases to the wall temperature and does not change when the helical angle exceeds 720°. Moreover, within the mass flow rate range of 1.6 g/s to 3.2 g/s, an increase in the mass flow rate was found to enhance the heat transfer performance of the helical tube. This study provides a reference for the selection and application of a helical tube under intermittent flow conditions and also contributes to the experimental research of inter-wall heat exchanger and pulse tube expansion refrigerators.