The non-premixed steady flamelet model is extended by two simple, robust and effective heat loss modelling approaches. The heat release damping (HRD) approach decreases the chemical source term in the energy equation by a constant factor, while the artificial radiation (AR) approach introduces an augmented temperature dependent radiative source term. The models are tested in a simulation of the 0.78 MWth IFRF (International Flame Research Foundation) pilot scale, non-premixed, natural gas/oxygen flame. Both approaches are applied in steady laminar flamelet calculations with detailed chemistry, tabulating the thermo-chemical state as a function of mixture fraction and normalised heat loss. The turbulence-chemistry interaction is modelled using the beta-PDF approach. An enthalpy transport equation is solved to keep track of the heat loss, while radiative heat transfer is calculated by the P-1 model. We observe that the major species, temperature, velocities and velocity fluctuations show a good agreement with the available experimental data. The heat loss modelling yields a significant improvement over the adiabatic model. Interestingly, both heat loss models (HRD and AR) show negligible differences in the simulations of the turbulent flame and permit to apply the steady laminar flamelet model to oxy-fuel processes in a simple, robust and user friendly manner.