The stabilization of a premixed methane/air flame in a narrow quartz tube strongly depends on the thermal environment, and particularly on heat transfers between the wall and the gas. Such a coupling induces unsteady behaviours that have only been observed at mesoscale. The aim of this study is then to simulate this coupling by solving simultaneously the one-dimensional equations driving fluid and solid properties with complex chemistry. To validate the numerical simulations, an experimental test case is built. A cylindrical quartz tube has been used with a 5mm inner diameter, chosen above the conventional quenching diameter of the premix. An original unsteady phenomenon is observed experimentally: from a steady reactive configuration, a heat source is activated on the tube's external wall upstream from the flame, lasting few seconds. It makes the flame front move towards upstream until it reaches the maximum wall temperature imposed. The simulations predict well this behaviour proving the ability of the numerical strategy to compute unsteady couplings with different time scales and give access to all the variables as functions of time and space. This highlights new way of controlling a flame position in a channel by a localized and temporary heat input.