The classical problem of the ignition and flame generation of combustible premixed gases by a hot flat plate is analyzed by asymptotic techniques for moderate values of the Zeldovich numbers. For temperatures of the plate smaller than the adiabatic flame temperature it was found that the corrections to the zeroth-order solution (Zeldovich approximation) are very important for finite Zeldovich numbers. The asymptotic analysis was carried out with the inclusion of reactant consumption showing different responses depending if the reactant consumption parameter is larger or smaller than a critical one. For temperatures of the plate larger than the adiabatic flame temperatures (that is, the reactant consumption parameter larger than the critical one), the ignition is not characterized by a thermal runaway and a smooth transition from frozen to equilibrium flow is obtained. The evolution towards the premixed flame formation is analyzed and the flame position and flame temperature are obtained.