A transient model is developed to study the evaporation of a liquid microlayer under a growing vapor bubble during nucleate boiling on the surface of a flat composite wall. The wall consists of a thin. volumetrically heated metallic foil or film and a Pyrex glass substrate or thin coating. The model predictions are qualitatively in agreement with experimental data for a water microlayer evaporation on a SnO2 coated Pyrex glass plate. Results for a heated metal foil on a Pyrex glass substrate show that the local heat flux at the solid-liquid-vapor triple point could be as much as one to two orders of magnitude higher than the input heat flux. Consequently, the wall temperature at the triple point drops rapidly, resulting in a non-uniform wall surface temperature. Both the accommodation coefficient of evaporation and lateral heat conduction in the heated wall significantly affects the liquid microlayer evaporation on a thin, highly conductive wall, especially during the early stage of the bubble growth. As either the thickness or the thermal conductivity of the heated wall is increased. the evaporation rate increases due to improved lateral heat conduction, approaching that for an isothermal wall. Conversely, a thin coating of low conductivity material significantly reduces the evaporation rate of the liquid microlayer, whereas the effect of the thermal properties of the heated metallic substrate is negligible unless the coating is very thin.