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Experimental investigations in engines as well as in much simpler environments such as constant volume combustion chambers concerning the influence of combustion chamber wall insulation on engine efficiency have produced conflicting statements about the magnitude of the wall heat flux during quenching and its trend with respect to wall temperature. Present engine codes model quenching, if at all, using simple chemistry assumptions (that fail already to explain the correct behavior for laminar head-on quenching) with matching conditions that are more based on pragmatic than physical grounds. It seems thus desirable to have as an aid for future engine code design a complete understanding of the physical processes occuring in the flame wall interaction zone as well as of the appropriate boundary conditions.