The laminar flame speeds and structures of near-limit autoignition-assisted cool and warm n-heptane/air flames at different ignition Damkӧhler numbers which are the ratios between flow residence time and the ignition delay time, elevated temperatures and pressures are studied computationally and analytically over a broad range of equivalence ratios. The primary objective of this work is to understand the effects of the ignition Damkӧhler number, mixture temperature, equivalence ratio, and pressure on the dynamics and structures of cool and warm flame propagation near the flammability limit. Different transitions among near-limit cool, warm, and hot flames are examined. The results show that both cool and warm flame structures and propagation speeds change dramatically with the increase of the ignition Damkӧhler number. Moreover, the dependence of normalized cool and warm flame speeds on the ignition Damkӧhler number is affected by the equivalence ratio, pressure, and flame regimes. Furthermore, for equivalence ratios within the hot flame flammability limits, the results show that there exist two flame speeds, one for the hot flame and the other for the cool flame. It is shown that the cool flame speed has a non-monotonic dependence on the initial mixture temperature due to the negative temperature coefficient (NTC) effect. However, the warm flame speed has a much weaker NTC effect and the hot flame speed only increases monotonically with the increase of the initial temperature. The results also reveal that the lean cool flame speed can be much higher than the hot flame speed near the NTC region. Finally, a simple analytical model for predicting the flame speed of autoignition assisted flames is developed. The model implies that the reduced activation energy of autoignition strongly affects the flame speed dependence on the ignition Damkӧhler number. The present results significantly advanced the understanding of the near-limit low temperature flame dynamics.