A mathematical model to describe the coupled heat transfer in effusion-cooled combustor walls is presented. A heat balance with respect to the heat transfer with film cooling on the hot side, heat transfer on the cold side and heat exchange between the wall and the coolant inside the holes leads to a system of four equations for the unknown temperatures on the hot and cold side of the wall and for the inlet and exit temperature of the coolant. The model is validated with experimentally determined exit temperatures. A parameter study showing the influence of the major dimensionless parameters is performed.