Owing to their chemical resistance, fused silica and borosilicate are used for many applications in the chemical and medical industries. The flat or hollow glass components are welded to complex devices. State of the art is a manual process using a gas flame. For the welding of complex quartz and borosilicate glass devices, the manual process must be performed by an experienced welder. In addition, the gas flame has a low energy efficiency, affects the chemical composition of the glass and only allows a limited level of automation. This study employs a CO2 laser beam source for the glass joining process to enable a high automation level. During the joining process, the laser power is controlled by non-contact temperature measurement, such that a constant viscosity is maintained throughout the welding process by stabilizing the glass temperature. The glass powder supplied is used as filler material to bridge gaps in complex geometric joining applications. The results prove that applying the glass powder leads to a homogeneous weld seam of a constant height. Seam collapse due to insufficient gap bridging did not occur while welding with powder additive. After welding, a subsequent thermal treatment removed the residual stress in the welded quartz glass connections. In order to prevent the glass from breaking when producing borosilicate glass connections, the components were preheated to the annealing temperature before the actual joining process. Combining CO2 laser radiation and glass powder fillers for temperature-controlled glass welding processes is expected to be introduced as an automated fusion process in the near future.