The limits to self-sustaining catalytic combustion in a microscale channel were studied computationally using a cylindrical tube reactor. The tube, 1 mm in diameter, 10 mm long, and coated with Pt catalyst, was assumed to be thermally thin, and the boundary condition on the wall was set to be either adiabatic or non-adiabatic with fixed heat transfer coefficient. Methane/air mixtures with average velocities of 0.0375–0.96 m/s (corresponding to Reynolds number, Re, ranging from 2.5 to 60) were used. When the wall boundary condition was adiabatic, the equivalence ratio at the extinction limit monotonically decreased with increasing Re. In contrast, for non-adiabatic conditions, the extinction curve exhibited U-shaped dual limit behavior, that is, the extinction limits increased/decreased with decreasing Re in smaller/larger Re regions, respectively. The former extinction limit is caused by heat loss through the wall, and the latter is a blow-off-type extinction due to insufficient residence time compared to the chemical timescale. These heat-losses and blow-off-type extinction limits are characterized by small/large surface coverage of Pt(s) and conversely large/small numbers of surface coverage of O(s). It was found that by diluting the mixture with N2 rather than air, the fuel concentration and peak temperatures at the limit decreased substantially for mixtures with fuel-to-oxygen ratios even slightly rich of stoichiometric because of a transition from O(s) coverage to CO(s) coverage. Analogous behavior was observed experimentally in a heat-recirculating “Swiss-roll” burner at low Re, suggesting that the phenomenon is commonplace in catalytic combustors near extinction. No corresponding behavior was found for non-catalytic combustion. These results suggest that exhaust-gas recirculation rather than lean mixtures are preferable for minimizing flame temperatures in catalytic microcombustors.