A new approach for modeling turbulence-radiation interaction is proposed. The formulation is based upon equations for statistical moments. Additional to the balance equations for the velocity and mixture fraction, equations for the mean, variance, covariance of heat release rate, and mixture fraction is solved. The coupling with the chemistry model is formulated by means of a two dimensional pdf of mixture fraction and heat release rate. The proposed approach is open for improvement by more sophisticated submodels. A natural gas fired combustion chamber is designed and constructed, and the temperature field measured by CARS spectroscopy. The main features of the modified combustion system are discussed. The comparison of experimental temperatures with the numerical simulation of the combustion system shows the good quality of our approach. The modeling of the two dimensional pdf is found to be most suitable for the hot region near the burner, where most radiation effects take place.