Abstract Based on the superposition principle, we propose in this study a Monte Carlo (MC) formulation for radiative transfer in quasi-isothermal media which consists in directly computing the difference between the actual radiative field and the equilibrium radiative field at the minimum temperature in the medium. This shift formulation is implemented for the prediction of radiative fluxes and volumetric powers in a combined free convection–radiation problem where a differentially heated cubical cavity is filled with air with a small amount of H2O and CO2. High resolution spectra are used to describe radiative properties of the gas in this 3D configuration. We show that, compared to the standard analog MC method, the shift approach leads to a huge saving of required computational times to reach a given convergence level. In addition, this approach is compared to reciprocal MC formulations and is shown to be more efficient for the prediction of wall fluxes but slightly less efficient for volumetric powers.