A method for thermal process management, with the support of which at least one three-dimensional article is producible by additive manufacture, by discharging a certain quantity of volume elements (110, 120) per unit time of at least one fluid solidifiable material at a certain temperature using at least one discharge nozzle of at least one discharge unit of a device that is controllable by the method, for producing the at least one three-dimensional article at discrete positions in a construction chamber according to a previously established model of the three-dimensional article, wherein the model of the three-dimensional article is part of a computer-implemented machine code that defines the discrete positions of the volume elements to be discharged and boundary conditions for their discharge, and wherein for each discrete position in three-dimensional space the temperature of the volume element is calculated, taking into account the thermal energies that are input into and removed from the construction chamber by at least one heat source and at least one heat sink respectively and released in the construction chamber by heat losses, characterised in that the method comprises the following steps: - determining whether the calculated temperature of the current volume element at the current point in time and at the current discrete position is within a material-specific interval, - determining whether the calculated temperatures of the adjoining volume elements (120, 150) over an observed time interval from a previous to the current point in time are below a material-specific upper limit for temperature, - if the calculated temperature at the location of the current volume element is within the material-specific interval and the temperatures of the adjoining volume elements (120, 150) over the observed time interval are below the material-specific upper limit for temperature: • continuing to determine the temperature of the next volume element at the next discrete position at the next associated discrete point in time, • continuing to determine the temperatures of the adjoining volume elements (120, 150) until the next associated discrete point in time, - if the calculated temperature at the location of the current volume element is outside the material-specific interval or the temperatures of the adjoining volume elements (120, 150) over the observed time interval are above the material-specific upper limit for temperature: • adapting the machine code and the boundary conditions for an increase and decrease in temperature, at least at the current discrete position, • continuing to re-determine the temperature of the current volume element at the current discrete position, • continuing to re-determine the temperatures of the adjoining volume elements (120, 150), wherein the steps for at least part of the model of the three-dimensional article are performed. - determining whether the calculated temperature of the current volume element at the current point in time and at the current discrete position is within a material-specific interval, - determining whether the calculated temperatures of the adjoining volume elements (120, 150) over an observed time interval from a previous to the current point in time are below a material-specific upper limit for temperature, - if the calculated temperature at the location of the current volume element is within the material-specific interval and the temperatures of the adjoining volume elements (120, 150) over the observed time interval are below the material-specific upper limit for temperature: • continuing to determine the temperature of the next volume element at the next discrete position at the next associated discrete point in time, • continuing to determine the temperatures of the adjoining volume elements (120, 150) until the next associated discrete point in time, • continuing to determine the temperature of the next volume element at the next discrete position at the next associated discrete point in time, • continuing to determine the temperatures of the adjoining volume elements (120, 150) until the next associated discrete point in time, - if the calculated temperature at the location of the current volume element is outside the material-specific interval or the temperatures of the adjoining volume elements (120, 150) over the observed time interval are above the material-specific upper limit for temperature: • adapting the machine code and the boundary conditions for an increase and decrease in temperature, at least at the current discrete position, • continuing to re-determine the temperature of the current volume element at the current discrete position, • continuing to re-determine the temperatures of the adjoining volume elements (120, 150), • adapting the machine code and the boundary conditions for an increase and decrease in temperature, at least at the current discrete position, • continuing to re-determine the temperature of the current volume element at the current discrete position, • continuing to re-determine the temperatures of the adjoining volume elements (120, 150),