The method of overlapping neutron spectra has been developed by Selengut to calculate neutron spectra and reaction rates in weakly absorbing media with temperature discontinuities. A combination of Selengut's method with multicollision probability theory leads to a new thermalization method suitable to a wider field of application, especially to the homogenization of reactor cells. Based on this theory, the code THERMAL has been written. The results of THERMAL have been compared with those of the standard transport code THERMOS. Comparison of the results gave a satisfactory correspondence. Compared to THERMOS, the computing time and the storage capacity requirements of THERMAL are fairly small.