Growing interest in small-scale, portable energy systems such as fuel cells has necessitated the development of small-scale fuel processing or reforming systems. Many fuel reforming systems require reliable heat sources as in some cases temperatures in excess of 600°C maybe required. Sub-millimeter combustors can provide such a heat source; however, a broader set of design rules are needed for constructing systematically engineered heat sources. In this article, experimental observations and computational fluid dynamics modeling results are presented for stable and steady confined flame structures within an alumina sub-millimeter combustor. Influence of inlet flow and thermal boundary conditions are evaluated through a parametric study. The inlet flow rates and relative gas composition, the thermal boundary conditions that include thermal conductivity of the walls, convection of heat to and from the walls, and radiation of heat energy through the walls all determine the position, structure, and temperature of the reacting fluid and combustor walls. The model shows the importance of radiative heat transfer in the formation of the steady-state flame structures within the microcombustor.