Method for a layer-wise construction of a three-dimensional object from a building material in powder form by means of a sequential solidification of layers of the building material in powder form at those positions of a layer that correspond to a cross-section of the object, wherein the solidification is effected by introducing heat energy and the method for each layer comprises the following steps: a step of providing a layer of a building material in powder form on a building support or a layer that has been previously solidified at selected positions, a step of pre-heating the applied building material up to a pre-heating temperature below the temperature at which the material is solidified and a step of solidifying the applied layer by means of electromagnetic radiation or particle radiation , in which step a solidification radiation incidence region sequentially sweeps over all positions of the layer corresponding to the cross-section of the object so that the powder at these positions is solidified by the heat energy introduced by the radiation, characterized in that in the solidification step, which already starts before the applied powder layer has reached a desired working temperature, the heat energy introduced per unit area in the solidification radiation incidence region is reduced with time during a predetermined period the start of which coincides with the start of the solidification step and can be described by a function monotonically decreasing with time in that the heat amount introduced per unit area is reduced by reducing the radiant flux in the solidification radiation incidence region that is sweeping over the powder and/or the heat amount introduced per unit area is reduced by an increase of the speed with which the solidification radiation incidence region sweeps over the powder layer. a step of providing a layer of a building material in powder form on a building support or a layer that has been previously solidified at selected positions, a step of pre-heating the applied building material up to a pre-heating temperature below the temperature at which the material is solidified and a step of solidifying the applied layer by means of electromagnetic radiation or particle radiation , in which step a solidification radiation incidence region sequentially sweeps over all positions of the layer corresponding to the cross-section of the object so that the powder at these positions is solidified by the heat energy introduced by the radiation, in the solidification step, which already starts before the applied powder layer has reached a desired working temperature, the heat energy introduced per unit area in the solidification radiation incidence region is reduced with time during a predetermined period the start of which coincides with the start of the solidification step and can be described by a function monotonically decreasing with time in that the heat amount introduced per unit area is reduced by reducing the radiant flux in the solidification radiation incidence region that is sweeping over the powder and/or the heat amount introduced per unit area is reduced by an increase of the speed with which the solidification radiation incidence region sweeps over the powder layer. <EOS>