A holding device is presented in which a layer which is to be oxidized is processed, in a single-substrate process. The process temperature during the processing is recorded directly at the substrate or at a holding device for the substrate. The process includes introducing a substrate, which bears a layer to be oxidized uncovered in an edge region in a layer stack, into a heating device, passing an oxidation gas onto the substrate, heating the substrate to a process temperature, which is recorded during the processing via a temperature of the holding device which holds the substrate, and controlling the substrate temperature to a desired temperature or temperature curve during the processing.