Flame quenching plays a central role in pollutant formation and remains challenging to model, especially near cooled walls, where CO levels increase. Precise modeling of flame–wall interaction is necessary, since heat losses to the wall can influence both performance and emissions. Flamelet-Generated Manifolds (FGM) efficiently tabulate detailed chemistry, but they often omit the combined effects of strain, heat loss, and mixing with exhaust gas, which limits their ability to predict near-wall extinction. While heat loss modeling in FGM is established [1, 2, 3, 4], recent studies addressed individual components of this problem: exhaust-gas mixing has improved near-wall CO predictions [5], and variable strain rate and enthalpy have shown clear benefits in a turbulent configuration [6, 7]. The four-dimensional FGM developed in this study investigates the coupled influence of strain and heat loss in premixed methane-air combustion. The proposed approach uses the counterflow premixed configuration, and expands the state space through: (i) a CO2-based progress variable capturing reaction progress; (ii) a strain-sensitive intermediate species obtained by varying flamelet mass-flow rates; (iii) a normalized enthalpy coordinate representing heat-loss-induced temperature reductions; and (iv) the mixture fraction. Together, these controls are intended to improve the modelling of local extinction pathways relevant to wall quenching. The manifold is generated in Cantera using the detailed GRI-Mech 3.0 mechanism, and the solver is based on OpenFOAM v10. A laminar V-shaped side-wall-quenching experiment [8] at atmospheric conditions, in which one flame branch interacts with a cooled wall, is used for validation. Comparisons are made with measured temperature profiles, CO concentrations, and wall heat flux. This work advances a physics-rich FGM for flame–wall interaction, enabling improved pollutant prediction and future extensions to turbulent flows.