If the flame temperature and the reaction speed can be controlled arbitrarily, it is of great help for energy saving through effective utilization of heat generated by combustion. In order to examine the possibility of such mild or moderate combustion, we tried to identify possible weakest flames experimentally with heated meso-scale channel, that is, combustion with controlled heat balance. Results show that the lowest flame speed may exist even though heat loss is compensated by the external heating. For the case of low flow velocity condition, the temperature difference between heated channel wall surface and flame measured by using thermocouple became smaller and smaller with decreasing flow velocity. It implies that there is the lowest flame temperature which corresponds to ignition temperature. To further examine existence and its mechanism of the lowest flame speed, 1-D computations with detailed chemistry were conducted. Computational results show a limit of stable solution in the low velocity region as well as experimental results. Furthermore, diffusive mass transfer was dominant compared to convective mass transfer in the low velocity region. It is probably related to the existence of the lowest flame speed, since the radical species, which is vital for chain reaction, diffuse out from reaction zone.