The flamelet generated manifold (FGM) model is suitable for moderate or intense low oxygen dilution (MILD) combustion provided the flamelets underlying the manifold include the effects of strong dilution by products of the fuel/oxidizer mixture. Here we propose such an extended model based on the use of non-premixed flamelets diluted at the airside and develop its application to non-adiabatic combustion in a lab-scale furnace. The extended model is referred to as diluted air FGM (DA-FGM) model. In the DA-FGM model in addition to mixture fraction, progress variable and scaled enthalpy loss, one additional controlling parameter named air dilution level, is introduced leading to a four-dimensional lookup table for laminar flames. For turbulent flames also variances of mixture fraction and progress variable are taken into account as independent variables leading to a six-dimensional table. Using a RANS approach implemented in OpenFOAM-2.3.1, the DA-FGM model has been applied to MILD combustion of Dutch natural gas in a lab-scale furnace operated at a thermal power 9 kW and at equivalence ratio 0.8. Radiation is described using a weighted-sum-of-gray-gases (WSGG) model. The validation study is mainly done using a grey WSGG model with TRI taken into account. The relative importance of including turbulence radiation interaction (TRI) and spectral treatment of radiative transfer is also studied. The predicted velocity and temperature statistics are in good agreement with the experimental LDA and CARS data provided not only the mixture fraction fluctuations but also the progress variable fluctuations are taken into account.