The combustion and soot processes in a fluidized-bed (FB) - like furnace are studied numerically. Fuel considered is methane. The simulation results obtained show that the most important sooting region in the furnace is the lower circulating region formed between the secondary air jets and the primary inlet of the furnace (referred to here as the FB-region), The most important factor affecting the soot formation in this FB-region are local temperatures in the stagnation point - like flow region formed in the middle of the furnace between the two opposing secondary air jets. These temperatures affect soot inception in this region, as well as local temperatures in the FB-region. Turbulent temperature fluctuations are high enough, so that they have important favoring effects on soot formation in the important sooting regions indicated above, By accounting for radiation heat transfer in the simulation, temperatures in the hottest sites along the central symmetry plane of the furnace are reduced, roughly, by about 100 K. This has significant adverse consequences on total soot amounts generated; soot amounts generated in this case are about 10 times lower than those predicted when radiation effects are ignored. Nevertheless, soot levels in the furnace, even under radiating conditions, are still clearly higher than those typical for normal methane diffusion flames under atmospheric pressure. In contrast to the case when radiation is not simulated, under radiating conditions decoupling soot from the gas phase is found to have almost no noticeable impact on local temperatures and species concentrations. In this case, however, less heat will be radiated to the walls and to colder regions in the furnace.