Open-cell foams are promising catalyst supports as they provide a low pressure drop, radial mixing, and exceptional heat transport properties. Even though their large potential for the design of small-scale, dynamically operated reactors with strongly exothermic reactions is known, their application is not yet common. To design efficient and safe structured reactors in the future, the understanding of structure-heat transport relations is key. Fully resolved CFD simulations of non-isothermal structured reactors including chemical surface reactions require a high modeling effort and are computationally expensive. In a previous study we therefore implemented volumetrically distributed heat sources in the solid to mimic the heat production during an exothermal reaction, and evaluated the resulting heat flows and temperature distributions via CFD. The previous analysis, however, was limited to one specific open-cell foam geometry. In this study, we extend the conjugate heat transfer problem including heat production in the solid to five periodic open-cell foams (Kelvin cell-lattices) with defined but different structural parameters to establish structure-heat transport relations. We confirmed conduction being the dominant heat removal mechanism and found the strut diameter and the solid thermal conductivity being the key parameters to improve heat transport and reduce hot spots.