The temperature inside the cylinder of a methanol-fuelled single-cylinder research engine running under knocking conditions is measured by means of Coherent Anti-Stokes Raman Scattering (CARS) spectroscopy, and the pressure is measured with a piezoelectric transducer. In order to obviate any errors arising from possible deficiencies in the spectral scaling laws which are commonly used to represent nitrogen Q-branch CARS spectra at high pressure, a purely experimental technique is employed to derive temperatures from CARS spectra by cross-correlation with a reference library of spectra recorded in an accurately calibrated high-pressure high-temperature optical cell. - The temperature and pressure profiles measured in the running engine are then used as input data for chemical kinetic modeling of the endgas autoignition. Exactly the same exhaustive chemical mechanism and exactly the same rate coefficient expressions are used for the autoignition modeling as are employed in Part I [1] for the modeling of methanol flame velocities. A good qualitative understanding of the mechanism underlying endgas autoignition in the engine can be obtained, although the calculated autoignition point occurs slightly earlier than the observed point. - The importance in the autoignition mechanism of hydroperoxyl radical reactions and of the thermal decomposition of hydrogen peroxide is demonstrated by means of a sensitivity analysis. - For purposes of comparison, the autoignition modeling is also undertaken using earlier reaction schemes and rate coefficient data, notably those of Grotheer and Kelm (1989), Norton and Dryer (1989), Esser and Warnatz (1987), and Dove and Warnatz (1983). The discrepancies between results of the various models can be understood in terms of a very small number of sensitive reactions for which there are conflicting kinetic data.