To estimate materials' thermo−physical properties at high temperatures, there is a need of robust direct models that can be solved quickly and account for the strong coupling between conduction and radiation. This study investigates using the Monte Carlo method to solve a conduction−radiation model in a semi−transparent material in a reduced computational time. Transient conduction in an absorbing/emitting and non-scattering grey medium in an academic configuration is investigated. The radiative source term of the heat equation is estimated as a function of the temperature field to the power 4, using a Finite Differences algorithm and a single Monte Carlo simulation to solve radiation. The numerical study shows that the results are in good agreement with the literature and that the functional estimation of the radiative source term allows coupled model resolution in less computing time that the standard approaches, such as Finite Volumes or Elements Methods. Indeed, the coefficients of the function were obtained in 4h with the Monte Carlo computation on an academic calculation server. 15 different configurations were then solved in less than 1min in transient state configurations and less than 6min at steady state configurations with the Finite Differences Method on a conventional laptop. This function is obtained without any compromise on the complexity of the coupled physics or the geometry. Because of the latter features, using this method in inversion processes becomes easible, as the direct model must be evaluated a large number of times.