A hot foil stamping machine for stamping a foil onto a substrate (S), the stamping machine comprising: - a heating plate having a first surface (A1) and an opposite second surface (A2), - 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 (A5) and an opposite stamping interface surface (ASI), wherein the fifth surface (A5) of the stamping plate is attached to the second surface (A2) 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 (ASI) 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 (ASI) 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 (DPM) and a lumped-parameter model (LPM), 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 (ASI), provided by the state observer . - a heating plate having a first surface (A1) and an opposite second surface (A2), - 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 (A5) and an opposite stamping interface surface (ASI), wherein the fifth surface (A5) of the stamping plate is attached to the second surface (A2) 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 (ASI) 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 (ASI) 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 (DPM) and a lumped-parameter model (LPM), 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 (ASI), provided by the state observer . <EOS>