Self-recuperative burners are a common solution for efficient combustion systems in industrial furnaces. Due to the geometric complexity of the recuperators, a detailed CFD simulation is computationally expensive and not feasible for simulation models of burner-integrated systems such as radiant tubes. Especially in the FSI studies of radiant tubes, the temperature of the radiant tube surrounding the burner is decisive for the final results. The exclusion of the recuperator from the simulation models introduces significant uncertainties in the simulations results. The presented paper describes an innovative, efficient approach to model a fin-type recuperator in which the recuperator is geometrically reduced. The resulting acceleration of the numerical simulation makes a fully dynamic modelling of the recuperator in a radiant tube simulation possible. Specifically designed source terms are used to model pressure loss and heat transfer inside the recuperator to match results obtained with a detailed simulation model. The results show deviations in total heat transfer of less than 1.3% with a 98.5% reduction of numerical mesh size. The computational savings enable comprehensive modelling of air preheat for radiant tube simulations and accurately replicate flow and temperature profiles in the recuperator.