To provide insights into auto-ignition characteristics in low temperature combustion (LTC) engine conditions, computational singular perturbation (CSP) analysis is used to gain fundamental understanding into classification of ignition regimes in n-heptane air mixtures in the presence of temperature and composition inhomogeneities. Parametric studies are conducted using high-fidelity simulations with detailed chemistry and transport. In particular, a key interest is to understand different ignition behavior of the n-heptane mixture at the negative-temperature coefficient (NTC) versus the non-NTC conditions. The CSP analysis for the reference homogeneous system yields the number of exhausted modes (M) at various stages during the ignition event. In addition, the merging of two explosive modes is observed at the onset of auto-ignition. For the one-dimensional system, the M profiles along with the importance index (I^T) measured in the upstream of the ignition front are used to determine whether the front propagation is the spontaneous (I^T → 0) or deflagrative (I^T → 1) regime. At the relatively large temperature fluctuation considered herein, the mixture at non-NTC conditions shows initially a deflagration front which is subsequently transitioned into a spontaneous ignition front. For the mixtures at the NTC conditions which exhibit two-stage ignition behavior, the 1st stage ignition front is found to be more likely in the deflagration regime. On the other hand, the 2nd stage ignition front occurs almost always in the spontaneous regime because the upstream mixture contains active radical species produced by the preceding 1st stage ignition front. The effects of differently correlated equivalence ratio stratification are also considered and the results are shown to be consistent with previous findings.