A low dimensional Galerkin model is developed for the near wake behind a flameholder. The model represents the interactions between the von Kármán vortex shedding instability and a dynamic mean field correction. The instability is captured by the two leading proper orthogonal decomposition (POD) modes of the nonreacting attractor. A shift mode represents dynamic mean field corrections in the cold flow, and an expansion mode represents the added dilatation effects, in the reacting now. The model is used to demonstrate the attenuating effect of heat release on the instability: Under combustion, the POD Fourier coefficients, representing vortex shedding, are suppressed and the shift mode coefficient becomes increasingly negative, representing movement towards the steady solution.