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Based on the analysis of heat radiation intensity from flame,a new mathematical model of the tube-wall temperature of heated tubes is devel-oped by taking down-fired,upright-tube cylindrical furnace for example.The proposed mathematical model can be employed to indicate both the position and size of the hot spot at fire-facing wall of heated tube of combustion chamber,and is characteristic of sim-plicity and efficiency.If coupled with thermoelectric couple or infrared viewer,the presented location method of com-bustion hot spot can offer engineers very valuable proposal to keep furnace running more safely.The same is true for any other type of tubular furnaces.