this invention relates to an apparatus for regulating the heating of a thermoplastic band used in a station for thermoforming upwardly open containers , the apparatus being characterized in that , in a zone of the softened thermoplastic band , zone surrounded by a mesh of rigidified matter , the degree of deformation of this zone under the action of a predetermined mass is measured , the measured value of the degree of deformation is compared with a predetermined reference value corresponding to a good aptitude to thermoforming , and the heating of the band is regulated as a function of the value of deformation measured so that the deformation corresponds to the reference value .