This work reports the performance of an energy converter characterized by an emitting parallelepiped element with inside two, three, or five swirling connected combustion chambers. In particular, the idea is to adopt the heat released by H₂/air combustion, occurring in the connected swirling chambers, to heat up the emitting surfaces of the thermally-conductive emitting parallelepiped brick. The final goal consists in obtaining the highest emitting surface temperature and the highest power delivered to the ambient environment, with the simultaneous fulfillment of four design constraints: dimension of the emitting surface fixed to 30 × 30 mm², solar mode thermal efficiency greater than 20%, emitting surface peak temperature T > 1000 K, and its relative ∆T < 100 K in the combustion mode operation. The connected swirling meso-combustion chambers, inside the converter, differ only in their diameters. Combustion simulations are carried out adopting 500 W of injected chemical power, stoichiometric conditions, and detailed chemistry. All provide high chemical efficiency, η > 99.9%, and high peak temperature, but the emitting surface ∆T is strongly sensitive to the geometrical configuration. The present work is related to the “EU-FP7-HRC-Power” project, aiming at developing micro-meso hybrid sources of power, compatible with a thermal/electrical conversion by thermo-photovoltaic cells.