Combining low pressure drop and remarkable heat transport properties, open-cell foams offer a combination that makes them a highly attractive option as monolithic catalyst support. The coupled thermal behavior of foams and fluids during heat production, e.g., exothermic chemical reactions, is still not thoroughly described despite their potential to optimize temperature control in fixed-bed reactors. Hence, the aim of this study is to get deeper insight into coupled conjugate heat transfer and heat production in open-cell foams used in a tubular reactor with constant wall temperature. Therefore, we conducted - μCT-based CFD simulations of open-cell foams with artificial heat sources that mimic the heat of reaction during an exothermal chemical reaction and allow to study the effect of heat production on heat transfer while requiring lower computational cost than simulating actual chemical reactions. We implemented a range of heat source intensities, that covers typical exothermic reactions, to study their effect on heat flows as well as temperature fields and used CO2 methanation as a case study. We further quantified the influence of superficial velocity, heat source intensity, and material on the temperature fields inside the foam and found conduction being the dominant heat transport mechanism. We further evaluated the feasible range of even more simplified pseudo-homogeneous models and found high thermal conductivities and low superficial velocities to be appropriate. In conclusion, the presented approach offers the possibility to study thermal effects regarding catalytic supports and give valuable insight in heat transport mechanisms under relevant process conditions in heterogeneous catalysis (heat sources: 5–150 W for a reaction volume of 1.2 × 10−5 m3, superficial velocities 0–0.51 m s−1, thermal conductivities 5–50 W m−1 K−1).