The two-dimensional thermal convection with three-Pr series Ra number 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 a and c are obtained. Parameter a determines the basic characteristics of the temperature profile, and parameter c plays 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 c is the opposite to that of parameter a, and the c value decreases as the a value increases. The fitting parameters for the different Pr numbers have different distribution characteristics as the Ra number changes, but they have all suddenly decreasing interruptions, and as the Pr number becomes large, the characteristic Ra number for the interruption increases. The variation characteristic of parameter c is the opposite to that of parameter a. With the same Ra number, the larger the Pr number, 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 Ra number, and their corresponding characteristic Ra numbers are identical. The results show that the three have good correlation and are directly related to the change of flow pattern.