Abstract: To support experimental research into gas conversion by warm plasmas, models should be developed to explain the experimental observations. These models need to describe all physical and chemical plasma properties in a coupled way. In this paper, we present a modelling approach to solve the complete set of assumed relevant equations, including gas flow, heat balance and species transport, coupled with a rather extensive chemistry set, consisting of 21 species, obtained by reduction of a more detailed chemistry set, consisting of 41 species. We apply this model to study the combined CO2 and CH4 conversion in the presence of O2, in a direct current atmospheric pressure glow discharge. Our model can predict the experimental trends, and can explain why higher O2 fractions result in higher CH4 conversion, namely due to the higher gas temperature, rather than just by additional chemical reactions. Indeed, our model predicts that when more O2 is added, the energy required to reach any set temperature (i.e., the enthalpy) drops, allowing the system to reach higher temperatures with similar amounts of energy. This is in turn related to the higher H2O fraction and lower H2 fraction formed in the plasma, as demonstrated by our model. Altogether, our new self-consistent model can capture the main physics and chemistry occurring in this warm plasma, which is an important step towards predictive modelling for plasma-based gas conversion.