A one-dimensional model is developed and studied to explore the flame acceleration runaway mechanism for deflagration-to-detonation transition in thin tubes. This mechanism relies solely on the thermal feedback between the compression waves ahead of the flame and the temperature-sensitive laminar velocity of the flame. Within this model, the primary driver of the flame acceleration and compressive heating enhancement is the gas flow caused by the increased flame surface area. Results from the numerical integration of the reactive Navier–Stokes equations for perfect gases with a single-step chemical-kinetics model are compared with the solutions obtained when considering the flame as a steady-state discontinuity. The numerical results illustrate the flame acceleration runaway in finite time caused by a double feedback loop established in this model. The evolution of the flame acceleration towards a finite-time singularity eventually leads to the formation of a shock wave within the flame structure, triggering the onset of a detonation.