Turbulent burning velocities, flashback, and auto-ignition of turbulent n-heptane/air flames have been experimentally investigated with kHz-rate planar laser-induced fluorescence (PLIF) imaging. Using a reactor-assisted turbulent slot (RATS) burner and varying mixture equivalence ratios and mean jet velocities, turbulent flame structures and dynamics are investigated at two reactor temperatures, 450 and 650 K, with and without low-temperature ignition, respectively. Depending on the flow velocity and reactor temperature, two distinctive turbulent premixed flame regimes, namely, a chemically-frozen (CF) regime and a low-temperature-ignition (LTI) regime are observed. For the CF regime, the measured turbulent burning velocities demonstrate a near-linear relationship with the turbulent intensity fluctuations, whereas for the LTI regime, the turbulent burning velocities are found to be nonlinearly accelerated with the progression of low-temperature chemistry. With the onset of LTI, calculations show dramatic changes in mixture composition, laminar flame speed, and mixture Lewis number. Using a scaling analysis, relative contributions of transport, represented by the mixture Lewis number, and chemistry, represented by the laminar burning velocity, on the observed nonlinear increase of LTI turbulent burning speeds are evaluated. The analysis suggests that the increase of turbulent burning velocities for the LTI regime is attributed to both the increase of the laminar burning velocity and the decrease of the mixture Lewis number. It is found that the influence of increased laminar burning velocity due to the change of chemistry becomes more dominant with increasing equivalence ratio. At LTI conditions, accelerated flame propagation driven flashback and pre-flame auto-ignition, are identified and discerned using kHz-rate OH PLIF while increasing the mixture equivalence ratio from fuel lean to rich.