Detonation initiation and ignition wave propagation in concentration stratified n-heptane/air mixtures with and without temperature gradient are numerically modeled by using the correlated adaptive chemistry and transport (CO-DACT) method coupled with the hybrid multi-timescale (HMTS) method in a one-dimensional planar constant volume chamber. For concentration gradient only, three combustion modes, including spontaneous ignition, detonation to spontaneous ignition transition, and a fully developed detonation mode, are observed corresponding to low, critical, and high concentration gradients, respectively. It is shown that the onset boundary of the three combustion modes is strongly affected by the coupling between concentration and temperature gradients. It is found that at a given concentration gradient, the temperature gradient can either promote or inhibit the detonation formations, depending on the variation of the associated ignition delay times. A comprehensive criterion for the onset of different combustion models involving both concentration and temperature gradients is presented and verified numerically. The results show that the critical concentration gradient for detonation initiation is greatly modified by the existence of a temperature gradient and vice versa. The present results provide insights into knocking mechanisms in engines.