Practical combustion systems generally involve variations in enthalpy that influence burning rates and that may cause local quenching and enhanced pollutant emissions. A need exists for the study of simplified problems in which the effects of enthalpy variations are investigated in a controlled manner. The present work describes an analysis of the extinction of a turbulent flame between opposed streams with different enthalpies. One of these streams consists of a combustible gaseous mixture at ambient temperature while the other is an inert stream whose temperature may be varied. Thermochemical and mean reaction rate models are developed, assuming a thermal quenching mechanism to be operative, and the resulting expressions are evaluated with the help of a presumed pdf for product temperature. The describing equations which include a (k) over tilde-<(epsilon)over tilde> turbulence model are cast in similarity form and solved to determine an extinction condition. As extinction is approached the equations for mean flow and turbulence quantities reduce to the corresponding equations for an inert counterflow. An extinction parameter is determined as an eigenvalue of an equation describing the temperature rise due to combustion. Predictions are compared with published experimental data and qualitative agreement is found.