The Monte Carlo method is a powerful technique for simulating radiation heat transfer processes. The method can easily deal with irregular three-dimensional geometries, anisotropic scattering of radiation and other complexities, which are usually difficult to be tackled with other numerical techniques. On the other hand, Monte Carlo computations are highly time consuming. In addition, accurate radiation heat transfer solutions require that spectral properties be taken into account in a detailed manner, being the line-by-line integration the more accurate but also more computationally expensive technique. Due to these reasons, Monte Carlo computations that accurately consider the spectral properties of radiation are impracticable for several cases of interest in engineering. Therefore reducing the computer time associated to Monte Carlo simulations is highly desirable. This paper presents the Multi-Spectral Energy Bundle method, which reduces the computational time of Monte Carlo simulations in which the spectral properties are accurately taken into account. The method can be applied for line-by-line computations as well as along with spectral models. Here, the proposed method is applied with the accurate full-spectrum k-distribution method, and the obtained results are analyzed