A process for blow molding containers, in which a preform made of a thermoplastic material is subjected to thermal conditioning along a conveyance path in a heating line and then molded into a container in a blow mold by the action of blowing pressure, and in which the thermal conditioning is carried out by several radiant heaters arranged one above the other, wherein, after the container (2) has been blow-molded, a wall thickness is measured at at least one height level of the container (2), where the heating capacity of a radiant heater (41) only associated with this height level is automatically controlled, and where the automatic control system is supplied with a preassigned value for the wall thickness as the set point and the measured wall thickness as the actual value.