An empirical four-step mechanism has previously been proposed for describing ignition of heptane-air mixtures. This mechanism captures the low-temperature and high-temperature ignition behavior as well as the intermediate-temperature behavior, between roughly 800 K and 1100 K, where a negative temperature dependence of the overall rate is observed. The present paper derives simplified overall rate formulas for ignition times from this four-step mechanism and uses those formulas to derive a temperature-explicit model whose simplicity facilitates analysis of more complex ignition phenomena. Methods of activation-energy asymptotics are employed for the temperature-explicit model to investigate ignition in homogeneous, adiabatic systems, ignition by compressional heating in homogeneous systems, and structures and quasisteady propagation velocities of cool flames in weakly strained mixing layers. It is shown that, in the range of negative temperature dependence, there is a plateau in the ignition time when the criterion of thermal runaway is employed. Near this plateau region, cool flames with three-zone structures can propagate at velocities that increase with increasing initial temperature. Besides providing qualitative descriptions of ignition processes for hydrocarbon-air mixtures, the results lead to quantitative predictions that can be compared with experiment.