In industrial refinery furnaces, the efficiency of thermal transfer to heat crude oil before distillation is often altered by coke deposition inside the fuel pipes. This leads to increased production and maintenance costs, and requires better understanding and control. Crude oil fouling is a chemical reaction that is, at first order, thermally controlled. In such large furnaces, the predominant heat transfer process is thermal radiation by the hot combustion products, which directly heats the pipes. As radiation fluxes depend on temperature differences, the pipe surface temperature also plays an important role and needs to be predicted with sufficient accuracy. This pipe surface temperature results from the energy balance between thermal radiation, convective heat transfer, and conduction in the solid material of the pipe, meaning that the thermal behavior of the whole system is a coupled radiation–convection–conduction problem. In this work, this coupled problem is solved in a cylindrical furnace, in which the crude oil flowing in vertical pipes is heated. The thermal radiation of combustion gases is modeled using the discrete ordinate method (DOM) with accurate spectral models and is coupled to heat conduction in the pipe to predict its wall temperature. The flame is described with a complex chemistry combustion model. An energy balance confirms that heat transfers are effectively dominated by thermal radiation. Good agreement with available measurements of the radiative heat flux on a real furnace shows that the proposed approach predicts the correct heat transfers to the pipe. This allows an accurate prediction of the temperature field on the pipe surface, which is a key parameter for liquid fouling inside the pipe. This shows that the thermal problem in furnaces can be handled with relatively simple models with good accuracy.