The behavior of technically premixed CO2-diluted methane oxyflames is compared to operation with methane-air flames in a labscale combustor equipped with an axial-plus-tangential swirler. It has been shown in a former study that the stabilization regimes and topologies of CO2-diluted oxy-flames can be deduced from methane-air flames despite large changes of the oxidizer and fuel flowrates. This work proceeds and focuses on differences in distributions of wall temperature and wall heat fluxes for a methane-air and a CO2-diluted methane oxyflame sharing the same thermal power, equivalence ratio, adiabatic flame temperature and swirl number. Laser-Induced Phosphorescence measurements are used to determine the temperature distributions along the combustor metallic back plane wall and along the internal and external surfaces of the quartz windows. These data are used to determine the local heat flux through the combustor windows. It is found that both the air and CO2-diluted oxy-flames feature approximately the same temperature distributions and total thermal loads along the combustion chamber walls. As high concentrations of carbon dioxide are known to significantly enhance radiative heat transfer, an analysis is carried out so as to account for the mechanisms that provide this similarity in the wall temperatures and heat fluxes between the two flames. The low order model allows for determining the origin of the heat flux and shows how convective heat transfer is supplemented by radiative heat transfer when switching from air to CO2-diluted oxy-combustion with a global thermal load that remains roughly unaltered for the studied combustion chamber.