The feedback interaction between dynamic heat release and the acoustic characteristics of a combustor can produce an unstable 'self-excited' system that ultimately results in a steady pressure oscillation. A simplified model of this feedback loop is needed to predict the limit cycle frequencies and amplitudes. This paper is focused on the development of a physically-based, reduced-order, nonlinear heat release model for a burner-stabilized, laminar premixed flame in a laboratory combustor. Starting from the governing conservation equations, the heat release dynamics are described by partial differential equations that are simulated by a finite-difference method. Using proper orthogonal decomposition (POD) and a generalized Galerkin procedure, the infinite-dimensional PDE model can be reduced to a set of low-order nonlinear ordinary differential equations. The issues of model order versus accuracy and the selection of mode shapes to be used in the reduction are discussed. In addition, this theoretical model points out some major challenges that need to be faced when trying to identify an accurate nonlinear heat release model from experimental data. A two-mode linear acoustic model for the combustor is coupled to the unsteady heat release model and the resulting closed-loop response is compared to experimental data.