In this work, a first step in modeling and simulating the thermal behavior of an entire catalytic micro-monolith was performed. In particular, a Computational Fluid Dynamics (CFD) model was developed for simulating three-channel and five-channel micro-combustors. For both configurations, the operating maps were built as functions of the inlet gas velocity and compared to the operating map of a single-channel configuration.Results show that, due to the relevance of heat losses in micro-devices, it is not possible to extrapolate the behavior of the multi-channel configurations from that of the single channel. Therefore, simulation of the entire catalytic micro-monolith is needed. However, this is computationally demanding: it has been found that the CPU time almost linearly increases with the number of channels simulated.Finally, for a fixed total mass flow rate, it has been demonstrated the opportunity to maximize the overall fuel conversion by means of a non-uniform distribution of mass flow rates among the channels.