A setting welding device is set forth for setting stud-like auxiliary joining parts in a plurality of layers of material and subjecting them to a mechanical-thermoforming process on a second layer of material and connecting them to said second layer by way of a welding operation. For this purpose, the punch is used to apply to the welding auxiliary joining part mechanical and thermal loads that follow prescribed characteristic force and current curves. Furthermore, a corresponding connecting method that can be realized with the aid of the setting welding device is also disclosed.