In a known process for drawing a quartz glass strand, SiO2 particles are fed to a melting crucible and softened therein to form a quartz glass mass, and the softened quartz glass mass is pulled vertically downward as a quartz glass strand via a drawing nozzle which is provided in the bottom region of the melting crucible and has a gap-like drawing nozzle opening. In order, on the basis thereof, to make it easier to reproducibly produce a quartz glass strand with a minor deviation from the nominal wall thickness profile, and in particular to avoid irregularly occurring indentations and protrusions of the wall thickness profile, it is proposed according to the invention that the wall thickness profile of the quartz glass strand is detected, and that the drawing nozzle is heated by means of a plurality of heating elements which are distributed around the drawing nozzle opening and can be electrically actuated independently of one another, and that the quartz glass mass is locally heated by means of the heating elements within the gap-like drawing nozzle opening depending on measurement results of the wall thickness profile.