The response of a premixed laminar flame, stabilised in a narrow channel (ℓ i= 5 mm), is investigated for an amount of heat supplied upstream through the wall. The first objective is to determine the set of canonical problems that a reduced chemistry must accurately reproduce to simulate the flame/wall coupling under such circumstances. The second objective is to identify the major energy transport mechanisms at play, ie convective heat transfer in the gas or conductive in the solid wall. The stoichiometric methane-air flame numerical simulations performed include complex molecular transport and the fully coupled solving of heat transfer at and within the wall. Initially, the flame is stabilised by an inlet mass flow rate matching the flame burning velocity. A reference simulation is first performed with a comprehensive methane-air chemistry. Then, two chemistry reduction strategies targeting a different set of canonical problems are applied and the results compared to conclude on the necessary constraints for chemistry reduction under such flow configuration. Various heating intensities are considered and a minimum heating supply is found necessary to initiate a complete upstream flame translation. A specific attention is paid on the relative contributions of heat convection in the flow and heat conduction in the solid. The heat transfer mechanism triggering the flame movement is revealed to be mainly convective. The flame translation is found to be organised in two stages, with first a downstream movement due to fresh gases expansion because of heating by the wall, followed by the upstream propagation due to the enhancement of the burning rate by the preheating of the mixture. The shape, the flash back speed, and the final position of the flame vary with the amplitude of the heat flux brought to the external surface of the wall.