The main purpose of this paper is to analyze the heat transfer mechanism of a new type of regenerator with a low temperature difference and low current resistance under oscillatory flow at room temperature. Taking the single tube of the regenerator as the research object, the exact analytical solution of the radial heat transfer characteristics of the regenerator is obtained by studying its analytical model. The factors affecting the heat transfer characteristics are analyzed, and then the regenerator is optimized to improve the performance and efficiency of the regenerator system. In this study, we systematically analyzed the radial heat transfer characteristics of a regenerator under isochoric process conditions. A closed-system physical model of the incompressible isochoric process under oscillating flow was established. Then, the radial analytical solutions of pressure fluctuation, fluid velocity, fluid-solid temperature, and heat were derived in the complex number field. Furthermore, the fluid velocity, fluid-solid coupling wall temperature, heat, and equivalent heat transfer coefficient were assessed. Furthermore, the influences of frequency, inner diameter R1 of the regenerator, and different working medium and materials on the above parameters were discussed. It was found that the analysis and evaluation of fluid velocity, fluid-structure coupling wall temperature, heat, and equivalent heat transfer coefficient are helpful in understanding the dynamic characteristics of radial heat transfer in a regenerator system. Through the study of radial heat transfer under oscillating flow, it was found that the working medium, frequency, inner diameter of the regenerator, and material quality of the regenerator are helpful for the design optimization of the regenerator. Furthermore, our investigations established that the variation law of wall fluid-solid coupling temperature amplitude could be divided into three parts: the unidirectional flow part; the low-frequency part, where the temperature amplitude falls rapidly with increasing frequency; and the high-frequency part, where the temperature amplitude increases with the frequency. In addition, the variation of radial heat transfer of the fluid-solid coupling surface is similar to the changes in the temperature amplitude. We also discovered that the equivalent heat transfer coefficient of the fluid-solid surface is related to thermal conductivity of the material. Specifically, larger thermal conductivity values result in greater equivalent heat transfer coefficients. Based on the research into the radial heat transfer characteristics, the new regenerator has great application potential in the Stirling air conditioning system at room temperature.