A thermoforming device heats a plastic film to a substantially uniform temperature, in order to impart a curved shape to said film. The device includes a chamber, the internal pressure of which is variable and which is closed by the film, a system for measuring a sag in the film arranged outside the chamber and opposite said film, and a system for heating the film. The heating system includes a hot air blowing unit which is suitable for producing a hot airflow flowing parallel to the film between two opposite edges of said film.