The heat-transfer characteristics in the fireside of a pulverized-coal furnace are affected, among other factors, by the physical and chemical characteristics of the ash deposits. Indeed, the physical state of the ash deposits and their chemical composition determine the radiative and conductive properties of the furnace walls. Particularly, several complex mechanisms are involved in the radiative heat-transfer process at the walls that restricts the absorption of the incident radiation of the flame, particles, and hot gases. These mechanisms involve dependencies on the radiation spectrum due to the ash chemical composition and ash-sintering effects that enhance or hinder the overall heat transfer. In this paper, we discuss the complex mechanisms that describe the heat exchange in the presence of ash deposits and their impact on the prediction of the wall emissivity and ultimately the wall heat transfer in a real system.