Pre-ignition, involving complex interactions of physical and chemical processes, occurs not only in actual combustion engines but also in fundamental research equipment such as rapid compression machines and shock tubes. Thus, identifying the combustion conditions prone to pre-ignition is critical for the interpretation of ignition data and fuel design. Shock tube experiments with dimethyl ether (DME) were carried out in this study to investigate the pre-ignition behavior during fuel auto-ignition. The experimental conditions included a wide range of temperatures (620−1370 K), pressures (1−9 atm), and equivalence ratios (0.5−5.0). The results indicate that pre-ignition of DME is prone to occur in the transition region from a high temperature to an intermediate temperature (~1000 K), and the decrease in pressure and equivalency ratio will aggravate the pre-ignition behavior. Theoretical analysis was then performed using four physical-based criteria: temperature perturbation sensitivity of ignition delay times, thermal diffusivity, a dimensionless parameter analogous to the Damköhler number, and the Sankaran number. According to experimental observations and theoretical analysis, it was found that the temperature sensitivity (Stp = 75 μs/K) and Sankaran number (Sap = 1) are the best available criteria for predicting the pre-ignition behavior of negative temperature coefficient (NTC) fuels. The pre-ignition region of non-NTC fuels can be accurately predicted by thermal diffusivity and the Damköhler number, but they deviate greatly when predicting the pre-ignition of NTC fuels. This strategy is expected to provide a feasible method for identifying the critical conditions under which pre-ignition may occur and for revealing the pre-ignition mechanisms for other NTC fuels.