A hot foil stamping machine for stamping a foil onto a substrate, the stamping machine comprising: - a heating plate having a first surface and an opposite second surface, - at least one heating device for heating at least a region of the heating plate, - at least one temperature sensor for measuring a temperature of the heating plate, at least in a region of the heating plate, - at least one stamping plate having a fifth surface and an opposite stamping interface surface, wherein the fifth surface of the stamping plate is attached to the second surface of the heating plate, characterized in that the stamping machine comprises a control unit for controlling the temperature (T SI) of the stamping interface surface to a predefined desired temperature (T SI_D), wherein the control unit is configured to receive at least an actual temperature (T H_ACT) of the heating plate from the at least one temperature sensor and to provide a manipulated variable (u) to the at least one heating device, wherein the stamping machine further comprises a state observer for estimating an actual temperature ( T̂ SI_ACT) of the stamping interface surface of the at least one stamping plate based on at least one physics-based analytical model of the heat transfer between the heating plate and the stamping plate, wherein the physics-based analytical model is a hybrid model comprising a distributed-parameter model and a lumped-parameter model, and wherein the control unit further comprises a feedback controller for calculating the manipulated variable (u) for the at least one heating device based on the predefined desired temperature (T SI_D) and the estimated actual temperature ( T̂ SI_ACT)of the stamping interface surface, provided by the state observer. - a heating plate having a first surface and an opposite second surface, - at least one heating device for heating at least a region of the heating plate, - at least one temperature sensor for measuring a temperature of the heating plate, at least in a region of the heating plate, - at least one stamping plate having a fifth surface and an opposite stamping interface surface, wherein the fifth surface of the stamping plate is attached to the second surface of the heating plate, characterized in that the stamping machine comprises a control unit for controlling the temperature (T SI) of the stamping interface surface to a predefined desired temperature (T SI_D), wherein the control unit is configured to receive at least an actual temperature (T H_ACT) of the heating plate from the at least one temperature sensor and to provide a manipulated variable (u) to the at least one heating device, wherein the stamping machine further comprises a state observer for estimating an actual temperature ( T̂ SI_ACT) of the stamping interface surface of the at least one stamping plate based on at least one physics-based analytical model of the heat transfer between the heating plate and the stamping plate, wherein the physics-based analytical model is a hybrid model comprising a distributed-parameter model and a lumped-parameter model, and wherein the control unit further comprises a feedback controller for calculating the manipulated variable (u) for the at least one heating device based on the predefined desired temperature (T SI_D) and the estimated actual temperature ( T̂ SI_ACT)of the stamping interface surface, provided by the state observer.