This study focuses on exploring the thermochemistry in flame-wall interaction (FWI) for fully premixed side-wall quenching of a laminar, atmospheric-pressure dimethyl ether flame at equivalence ratio Φ=0.83 by simultaneous measurement of CO2 and CO mole fractions and gas phase temperature T. The applied laser diagnostics are dual-pump coherent anti-Stokes Raman spectroscopy (DP-CARS) targeting N2 and CO2, laser-induced fluorescence of CO and OH, as well as thermographic phosphor thermometry. The extension to DP-CARS to study FWI processes is the first of its kind, previous studies only provided (CO,T) measurements. The laser diagnostics are benchmarked and calibrated to an adiabatic test case and assessed in accuracy and precision. Subsequently, the approach is used to measure the thermochemistry close to a quenching wall. The nominal flame-to-wall distances from the experiment well match the numerical simulation data with a marginal offset of 20 µm. Conditioning the thermochemical data with respect to the instantaneous quenching point, named quenching-point conditioning, enables a novel tracing of the wall-parallel chemistry evolution across the quenching location. The study provides the first comparison of experimental three-scalar measurements (CO2,CO,T) with two-dimensional (2D) fully-resolved chemistry and transport (FCT) simulations. The validation of numerical simulations can now rely on the three scalars (CO2,CO,T) instead of the two scalars (CO,T) in past studies. The evaluation reveals that this novel three-scalar measurement allows highly sensitive probing of the thermochemical states and is clearly superior to the previously applied two-scalar approach. CO2 is less affected by the quenching wall compared to CO. Differential diffusion effects are experimentally confirmed by comparison to 2D-FCT, with the (CO2,T) state space being more sensitive than (CO,T). As the experimental methodology proved feasible for laminar operation, a transfer to turbulent cases, where the numerical analysis using direct numerical simulations (DNS) including FCT is limited, appears promising.