The formation and dynamics of premixed cool flames are numerically investigated by using a detailed kinetic mechanism of dimethyl ether mixtures in both freely-propagating and stretched counterflow flames with and without ozone sensitization. The present study focuses on the dynamics and transitions between cool flames and high temperature flames. The impacts of mixture temperature, inert gas temperature, and ozone concentration on low temperature ignition, cool flame formation, and flammable regions of different flame regimes are investigated. For the freely-propagating flames, three different flame structures (high temperature flames, double flames, and cool flames) are found. The present study shows that the flammability limit of dimethyl ether is significantly extended by the appearance of cool flames and that the conventional concept of the flammability limit of a high temperature flame ought to be reconsidered. Furthermore, the results demonstrate that the cool flame propagation speed can be significantly higher than that of near-limit high temperature flames and that ozone addition dramatically accelerates the formation of cool flames at low temperatures and extends the flammability limit. A schematic of a modified flammability limit diagram including both high temperature flames and cool flames is proposed. For stretched counterflow flames, the results also show that multiple flame regimes exist with and without ozone addition. It is demonstrated that at the same mixture enthalpy, ozone addition kinetically extends the cool flame extinction limit to a higher stretch rate. Moreover, with ozone addition, two different cool flame transition regimes: a low temperature ignition transition and a direct cool flame transition without an ignition limit at higher temperature, are predicted. The present results suggest that cool flames can be an important combustion process in affecting flammability limits and flame regimes as the mixture temperature, turbulent mixing, and radical production/recirculation are increased. The results also provide guidance in observing self-sustaining premixed cool flames in experiments.