Method for producing containers made of thermoplastic material from preforms, which defines a path for circulating the preforms and the containers, comprises: - a moulding unit for moulding containers having a vertical axis A comprising at least one blowing station, each including a mould with a cavity in the shape of a container and a device for injecting a pressurized fluid into the preform; - a heating unit for heating preforms which is located on the circulation path upstream of the moulding unit relative to the direction of circulation of the preforms, comprising: - a means for conveying the preforms comprising a plurality of individual supports for the preforms defining a path for heating the preforms; - a heating cavity comprising two lateral walls that face one another and are at a distance from one another, at least one of said walls being that which bears a plurality of radiation sources arranged one above the other and side by side facing the preforms, thereby forming a row of radiation sources relative to the path for heating the preforms; - an electrical power supply, supplying each radiation source with electrical power; - a control unit connected to the electrical power supply, said control unit having a memory for storing: - at least one electrical power setpoint for at least one row of radiation sources; - at least one thickness setpoint in at least one point of the container; - said control unit carrying out at least one measurement of the thickness (e) of a wall of the container at at least one point of said container by means of at least one sensor; characterized in that the control unit: - compares said thickness measurement (e) with said stored thickness setpoint; if said measured thickness (e) is different from the thickness setpoint, then the control unit modifies said electrical power of at least two rows of radiation sources while keeping the sum of the electrical powers being supplied to all of the rows of radiation sources the same. - a moulding unit for moulding containers having a vertical axis A comprising at least one blowing station, each including a mould with a cavity in the shape of a container and a device for injecting a pressurized fluid into the preform; - a heating unit for heating preforms which is located on the circulation path upstream of the moulding unit relative to the direction of circulation of the preforms, comprising: - a means for conveying the preforms comprising a plurality of individual supports for the preforms defining a path for heating the preforms; - a heating cavity comprising two lateral walls that face one another and are at a distance from one another, at least one of said walls being that which bears a plurality of radiation sources arranged one above the other and side by side facing the preforms, thereby forming a row of radiation sources relative to the path for heating the preforms; - an electrical power supply, supplying each radiation source with electrical power; - a control unit connected to the electrical power supply, said control unit having a memory for storing: - at least one electrical power setpoint for at least one row of radiation sources; - at least one thickness setpoint in at least one point of the container; - said control unit carrying out at least one measurement of the thickness (e) of a wall of the container at at least one point of said container by means of at least one sensor; - a means for conveying the preforms comprising a plurality of individual supports for the preforms defining a path for heating the preforms; - a heating cavity comprising two lateral walls that face one another and are at a distance from one another, at least one of said walls being that which bears a plurality of radiation sources arranged one above the other and side by side facing the preforms, thereby forming a row of radiation sources relative to the path for heating the preforms; - an electrical power supply, supplying each radiation source with electrical power; - a control unit connected to the electrical power supply, said control unit having a memory for storing: - at least one electrical power setpoint for at least one row of radiation sources; - at least one thickness setpoint in at least one point of the container; - said control unit carrying out at least one measurement of the thickness (e) of a wall of the container at at least one point of said container by means of at least one sensor; - at least one electrical power setpoint for at least one row of radiation sources; - at least one thickness setpoint in at least one point of the container; - said control unit carrying out at least one measurement of the thickness (e) of a wall of the container at at least one point of said container by means of at least one sensor; characterized in that the control unit: - compares said thickness measurement (e) with said stored thickness setpoint; - compares said thickness measurement (e) with said stored thickness setpoint; if said measured thickness (e) is different from the thickness setpoint, then the control unit modifies said electrical power of at least two rows of radiation sources while keeping the sum of the electrical powers being supplied to all of the rows of radiation sources the same.