This study developed a transient rutting analysis program based on the principles of heat transfer and the viscoelastic–viscoplastic theory of asphalt mixtures. Using the finite element model (FEM) model corresponding to the multi-layer pavement structure and the subprogram interface of ABAQUS software, along with Python programming, the program was designed to estimate rutting under transient temperature field conditions with climate conditions, traffic flow, and structure layer constitutive parameters of pavement considered. Subsequently, the program was used to validate the efficiency of the solution and analyze the influencing factors of internal temperature field and rutting depth within the asphalt pavement structure. Results showed that, based on meteorological data and recommended values of material thermal properties, the FEM of transient temperature field can accurately simulate the temperature field distribution of pavement structure. Based on loading information and dynamic modulus test, the transient temperature variable rutting with FEM proposed in this paper can simulate and calculate the rutting of pavement structure layer with some errors for different pavement conditions from 5% to 40%. Through parametric analysis of the influence factors of temperature field and rutting, the modified transient temperature field rutting prediction program can effectively simulate rutting of pavement structure, and the minor errors were less than 20%.