In this article, a numerical method for the simulation of radiative heat transfer is presented. The multiscale radiative exchange method (MREM) calculates the radiative source terms in a mesh structure that is coarser than the structures that are typically used in computational fluid flow calculations. To consider the effects of smaller scales on the overall predictions of the model, two dimensionless exchange factors are defined. An accurate simulation of self-extinction and rescattering in coarse volume cells is achieved if the exchange factors are used in the radiative energy balance. According to the location and size of each pair of coarse cells, integration elements of different sizes are used for the calculation of exchange factors. Therefore, the MREM takes into account the effects of a wide range of optical scales in its prediction. On the other hand, the MREM considers the radiative interaction between all of the geometric points in a quick and accurate manner. To improve the accuracy and the performance of the model, a mesh size analysis is performed and some sizes for various mesh structures are suggested for use in the MREM calculations. The model is verified by comparing it against some benchmarks. The predictions and computational cost of the method are compared to the results of other numerical methods, and the effects of different spatial scales on the accuracy of the method are addressed.