Sequential combustion architectures rely on auto-ignition flame stabilization in the second stage combustor. Due to the exponential temperature dependence of the ignition delay time the second stage flames can respond to hot spots generated by unsteady first stage combustion. In this paper, the auto-ignition flame response is investigated by extending an existing analytical model for acoustic waves so that it also accounts for entropy waves. Explicit expressions for the flame transfer functions and linear to non-linear transition thresholds are derived. Results for different operating conditions, forcing amplitudes and frequencies are discussed. For this, three computational domains of increasing complexity are considered for model validation: a 2D duct, a 3D backward facing step, and finally a full-scale Ansaldo Energia GT26 sequential combustor. Unsteady Reynold-averaged Navier–Stokes as well as large-eddy simulations are performed. Acoustic and entropic contributions of the flame response are separated by means of system identification techniques. Finally, non-linear flame transfer functions are identified. It is observed that the gains linearly increase with the excitation frequency and non-linear, frequency dependent effects are observed already for small amplitude levels of excitation.