In view of the limitations of the current calculation methods for thermal stress and low temperature critical cracking temperature of asphalt binder and in order to find a better method for calculating thermal stress and corresponding low temperature critical cracking temperature of asphalt binder, the 70^# matrix asphalt of four different origins was selected for rotating thin film oven (RTFO) and pressure aging vessel (PAV) tests. The creep compliance of the asphalt binder was obtained by BBR test. The thermal stress of the asphalt were obtained by two-step calculation method of Hopkins & Hamming algorithm and CAM model as well as one-step calculation method of Laplace transform respectively, and the corresponding low temperature critical cracking temperature was calculated based on SAP theory. Calculation results were compared and analyzed by statistical methods. The calculation methods were verified by correlation analysis and combined with measured road surface temperature data. Results show that the one-step calculation method of Laplace transform and the two-step calculation method of Hopkins & Hamming algorithm were in good agreement. The calculation result of p-value of low temperature critical cracking temperature based on t-test was more than 0.90. The Laplace transform one-step calculation method had a strong correlation with the BBR test. The correlation coefficients between the critical cracking temperature T_CR and the S/m index as well as the Huet rheological model index reached 0.84 and 0.94, respectively. The calculation results of the measured road surface temperature change data prove that the proposed method is not only suitable for uniform cooling conditions, but also for on-site continuous variable speed cooling conditions at any cooling rate.