Abstract Rising greenhouse gases (GHG) and decreasing anthropogenic ozone-depleting substances (ODS) are the main drivers of the stratospheric climate evolution in the 21st century. However, the coupling between stratospheric composition, radiation and dynamics is subject to many uncertainties, which is partly because of the simplistic representation of ozone (O₃) in many current climate models. Changes in ozone due to heterogeneous chemistry are known to be the largest during springtime in the Arctic, which is also a season with very active stratosphere–troposphere coupling. The focus of this study is to investigate the role of varying ozone levels driven by changing GHG and ODS for the Arctic polar cap stratosphere. We use two state-of-the-art chemistry-climate models with ocean coupling in two configurations (prescribed ozone fields vs. interactive ozone chemistry) for three different scenarios: preindustrial conditions—1 × CO₂, year 2000 conditions (peak anthropogenic ODS levels) and extreme future conditions—4 × CO₂. Our results show that in the upper and middle stratosphere CO₂ thermal cooling is the dominant effect determining the temperature response under 4 × CO₂, and outweighs warming effects of ozone by about a factor of ten. In contrast, in the lower stratosphere, the effects of O₃ warming and CO₂ cooling under 4 × CO₂ are largely offsetting each other. ODS driven variations in O₃ affect both the temperature mean and variability, and are responsible for the tight springtime coupling between composition and dynamics under year 2000 conditions in comparison to simulations under 1 × CO₂ or 4 × CO₂.