Microcombustion is one of the most essential topics in the development of micropower generators for portable devices, microaerial vehicles and sensors. Although one-dimensional numerical modelling of combustion has been developed, maturing a lot during the last forty years, two-dimensional numerical modelling of combustion, particularly at very small scales has only started in the last decade. In this particular study, two-dimensional numerical simulations of premixed, laminar, lean methane-air flames at atmospheric pressure formed in a 2 mm diameter microcombustor are performed. A skeletal mechanism consisting of 16 species and 41 reactions is employed. This study shows the importance of applying low target residuals for convergence in CFD, which plays a critical role in obtaining an accurate solution in the numerical modelling of microcombustion. The main focus of this work is to investigate the effect of preheating the reactants on the flame structure and stability with adiabatic and nonadiabatic combustor walls. The flame in the 2 mm diameter circular microcombustor under adiabatic wall conditions shows a laminar Bunsen type flame behaviour. On the other hand, under the nonadiabatic wall conditions, a cone shaped high temperature flame zone is observed. Preheating the reactants widens the flame stability at high incoming flow velocities under both conditions, however, under non-adiabatic wall conditions, at low incoming flow velocities and/or low mass flow rates, preheating the reactants contributes neither to flame stability nor combustion characteristics. On the contrary, it results in low combustor exit temperature. Finally, the effects of convective heat transfer coefficients and heat loss, with and without radiation, on the microcombustion are analysed. (C) 2015 Elsevier Ltd. All rights reserved.