[en] This paper adopts the Runge–Kutta ray tracing method to obtain the ray-trajectory numerical solution in a two-dimensional gradient index medium. The emitting, absorbing and scattering processes are simulated by the Monte Carlo method. The temperature field and ray trajectory in the medium are obtained by the three methods, the Runge–Kutta ray tracing method, the ray tracing method with the cell model and the discrete curved ray tracing method with the linear refractive index cell model. Comparing the results of the three methods, it is found that the results by the Monte Carlo Runge–Kutta ray tracing method are of the highest accuracy. To improve the computational speed, the variable step-size Runge–Kutta ray tracing method is proposed, and the maximum relative error between the temperature field in the nonscattering medium by this method and the benchmark solution is less than 0.5%. The results also suggest that the Runge–Kutta ray tracing method would make the radiative transfer solution in the three-dimensional graded index media much easier. - Highlights: • This paper adopts the Runge–Kutta ray tracing method. • The results by the Monte Carlo Runge–Kutta ray tracing method is of the highest accuracy. • The variable step-size Runge–Kutta ray tracing method is proposed.