This study employs a simplified analytical model to obtain qualitative predictions of transitions between non-adiabatic combustion regimes found in non-catalytic tubular micro-flow reactors, i.e. normal stable flames, flames with repetitive extinction and ignition (FREI), and weak flames that are stabilized by wall heat transfer. Assuming large activation energy for single-step kinetics, a comparison of exact solutions for constant and variable wall temperature profiles reveals that while a non-zero wall temperature gradient introduces a temperature lag, it has no impact on the structure of the flame solution itself. This result is significant as it establishes a link to quenching characteristics within heated micro-tubes, and further facilitates a simplified micro-flow reactor analysis. Predictions for sweeps of wall temperatures are combined to S-curves, which allow for a combustion regime classification for a given combination of micro-flow reactor geometry and mixture properties. A variation of parameters such as tube diameter or mixture stoichiometry yields predictions of shifts in regime transitions, thus providing insights on interactions between heat transfer and first order effects of chemical kinetics. A comparison to experimental data illustrates that the theoretical framework, - within inherent limitations, - captures qualitatively correct trends that reflect experimental observations, thus providing valuable insights for micro-flow reactor design and operation. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.