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There is a complex transition phenomenon in the flow field of a typical hypersonic vehicle, which has a significant impact on the performance of the vehicle. The effects of Mach number and wall temperature on the transition of HyTRV were studied by numerical simulation methods. The self-developed software of the research group was used to carry out numerical calculations. The range of Mach number was 3~8, and the range of wall temperature was 150~900 K. Firstly, the hypersonic corrections of the γ-$\mathop R\limits^ \sim $eθt transition model and the SST turbulence model were carried out. The pressure gradient coefficient correction and the high-speed cross-flow correction were introduced into the γ-$\mathop R\limits^ \sim $eθt transition model, and the compressibility corrections of the closure coefficients β* and β of the SST turbulence model were carried out. Then, the grid independence verification was carried out, and the modified numerical method and software platform were confirmed by comparing with experimental results. Finally, the effects of Mach number and wall temperature on the transition law of the HyTRV boundary layer were studied. The results show that the transition area is mainly concentrated on both sides of the upper surface and the center line of the lower surface. With the increase of the incoming Mach number, the starting position of transition on the upper and lower surfaces is greatly backward, and the turbulent zone is greatly reduced, but it still exists. At the same time, the friction coefficient of the laminar flow zone on the upper surface increases continuously, and the friction coefficient of the turbulent zone on the lower surface decreases. As the wall temperature increases, the starting position of transition on the upper and lower surfaces shifts forward, then rapidly shifts backward, and finally the turbulent zone almost disappears.