Method for operating a controlled thermostat of a cooling circuit of a driving combustion engine of a vehicle, the method comprising the following steps: a) measuring the temperature (T S) of the liquid coolant circulating in a first pipe of the cooling circuit at the outlet of the combustion engine, b) acquiring at least one item of information (C, N) representative of an operating parameter of the combustion engine, c) estimating the travel of the controlled thermostat by means of a numerical model modelling the exchange of heat between an electrical resistive element of the controlled thermostat and a rod of the controlled thermostat during the heating of the controlled thermostat by the resistive element, the exchange of heat between the rod and the wax of the controlled thermostat, the exchange of heat between the wax and the body of the controlled thermostat, the exchange of heat between the body of the controlled thermostat and the liquid coolant and drawing up a heat balance sheet for each part of the thermostat, d) estimating the temperature (T E) of the liquid coolant circulating in a second pipe of the cooling circuit at the inlet of the combustion engine as a function of the temperature (T S) measured in step a), of the information (C, N) acquired in step b), and of the travel estimated in step c), the second pipe being connected to a radiator with interposition of the controlled thermostat, a unit heater being connected to the second pipe, e) estimating the temperature (T 4) of the liquid coolant at the thermostat on the basis of the temperature (T E) estimated in the second pipe, the temperature (T 4) at the thermostat being obtained on the basis of the temperature (T E) estimated in the second pipe by correction by means of at least one coefficient determined as a function of a heating power of the unit heater, f) generating a useful voltage value to be applied to the controlled thermostat as a function of a temperature setpoint (T C), of the temperature (T S) measured in step a) and of the travel estimated in step c), g) applying the useful voltage (V C) to the controlled thermostat. a) measuring the temperature (T S) of the liquid coolant circulating in a first pipe of the cooling circuit at the outlet of the combustion engine, b) acquiring at least one item of information (C, N) representative of an operating parameter of the combustion engine, c) estimating the travel of the controlled thermostat by means of a numerical model modelling the exchange of heat between an electrical resistive element of the controlled thermostat and a rod of the controlled thermostat during the heating of the controlled thermostat by the resistive element, the exchange of heat between the rod and the wax of the controlled thermostat, the exchange of heat between the wax and the body of the controlled thermostat, the exchange of heat between the body of the controlled thermostat and the liquid coolant and drawing up a heat balance sheet for each part of the thermostat, d) estimating the temperature (T E) of the liquid coolant circulating in a second pipe of the cooling circuit at the inlet of the combustion engine as a function of the temperature (T S) measured in step a), of the information (C, N) acquired in step b), and of the travel estimated in step c), the second pipe being connected to a radiator with interposition of the controlled thermostat, a unit heater being connected to the second pipe, e) estimating the temperature (T 4) of the liquid coolant at the thermostat on the basis of the temperature (T E) estimated in the second pipe, the temperature (T 4) at the thermostat being obtained on the basis of the temperature (T E) estimated in the second pipe by correction by means of at least one coefficient determined as a function of a heating power of the unit heater, f) generating a useful voltage value to be applied to the controlled thermostat as a function of a temperature setpoint (T C), of the temperature (T S) measured in step a) and of the travel estimated in step c), g) applying the useful voltage (V C) to the controlled thermostat.