Burning carbon-free fuels such as hydrogen in gas turbines promises power generation with minimal emissions of greenhouse gases. A two-stage sequential combustor architecture with a propagation-stabilized flame in the first stage and an autoignition-stabilized flame in the second stage allows for efficient combustion of hydrogen fuels. However, interactions between the autoignition-stabilized flame and the acoustic modes of the combustor may result in self-sustained thermoacoustic oscillations, which severely affect the stable operation of the combustor. In this paper, we study an ‘intrinsic’ thermoacoustic feedback mechanism in which acoustic waves generated by unsteady heat release rate oscillations of the autoignition front propagate upstream and induce flow perturbations in the incoming reactant mixture, which, in turn, act as a disturbance source for the ignition front. We first perform detailed reactive Navier-Stokes (DNS) and Euler computations of an autoignition front in a one-dimensional setting to demonstrate the occurrence of intrinsic instability. Self-excited ignition front oscillations are observed at a characteristic frequency and tend to become more unstable as the acoustic reflection from the boundaries is increased. The Euler computations yield identical unsteady ignition front behaviour as the DNS computations, suggesting that inviscid mechanisms control the instability. In the second part of this work we present a simplified framework based on the linearized Euler equations (LEE) to compute the sound field generated by an unsteady autoignition front. Unsteady autoignition fronts create sources of sound due to local fluctuations in gas properties, in addition to heat release oscillations, which must be accounted for. The LEE predictions of the fluctuating pressure field in the combustor agree well with the DNS data. The findings of the present work are essential for understanding and modeling thermoacoustic instabilities in reheat combustors with autoignition-stabilized flames.