The two-dimensional thermal convection with three-Pr series Ranumber is calculated by using the highly efficient parallel DNS method. The two-parameter temperature boundary layer theory, with the pulsation influence taken into account, is used to fit the temperature boundary layer profile for the field averaged over all calculations. The distributions of the fitted parameters aand care obtained. Parameter adetermines the basic characteristics of the temperature profile, and parameter cplays a role in correcting the outer area of the temperature profile. Therefore, the simulation results of the temperature boundary layer profile is well matched with the theoretical solution in the 5 boundary layers. The variation characteristic of parameter cis the opposite to that of parameter a, and the cvalue decreases as the avalue increases. The fitting parameters for the different Prnumbers have different distribution characteristics as the Ranumber changes, but they have all suddenly decreasing interruptions, and as the Prnumber becomes large, the characteristic Ranumber for the interruption increases. The variation characteristic of parameter cis the opposite to that of parameter a. With the same Ranumber, the larger the Prnumber, the smaller the fitting parameter of the temperature profile is, indicating that the influence of pulsation in the temperature boundary layer is smaller. The heat transfer characteristic Nu/ Ra ^0.3, the large-scale circulation path circumference for the characteristics of plume movement, and the temperature boundary layer fitting parameter all have the interruptions with the change of Ranumber, and their corresponding characteristic Ranumbers are identical. The results show that the three have good correlation and are directly related to the change of flow pattern.