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. We have studied the quenching situation as it can be found in constant volume combustion chambers for a methane flame over a range of wall temperatures between 300K and 600K using Direct Numerical Simulation. To do this, we solved the fully compressible, one-dimensional Navier-Stokes equations with detailed mechanisms for kinetics and diffusion. This approach allows to compare various reaction schemes, to identify the most important species and reaction paths, and to investigate the influence of different modeling assumptions. The computational results show that the dimensional wall heat flux increases with wall temperature over the whole range of wall temperatures studied; this agrees well with the most recent measurements in a strongly improved experimental setup. It is found that the wall call be modelled as chemically inert and thermal diffusion processes are negligible for low wall temperatures between 300K and 400K. However, at higher temperatures, due to a dramatically increasing radical concentration (H, O, OH) at the wall, both become increasingly important leading to large heat release rates directly at the metallic wall surface of the combustion chamber, and can thus not be neglected in the modeling of the quenching process. Furthermore, these high radical concentrations adjacent to the wall indicate that the uncertainties in wall heat flux measurements at high wall temperatures could be underestimated by the experimentalists. The UHC concentration at a wall temperature of 600K is about 20 times smaller than for 300K after quenching.