To evaluate the contributions of different forcings to the temperature and atmospheric composition changes between 1980 and 2020, we exploited the chemistry-climate model (CCM) SOCOLv3. The study examined ozone content and atmospheric temperature response to (1) ozone-depleting substances; (2) greenhouse gas concentrations, ocean surface temperature, and sea ice coverage; (3) solar irradiance; and (4) stratospheric aerosol loading and, separately, (5) greenhouse gas concentrations, (6) ocean surface temperature and sea ice coverage, and (7) NOx surface emissions. To evaluate the impacts of specific factors, we performed model runs driven by each factor (1–7) variability as well as a reference experiment that accounted for the influence of all factors simultaneously. We identified the relative contribution of different factors to the evolution of the temperature and ozone content of the lower troposphere and stratosphere from 1980 to 2020. The model results were in good agreement with the reanalyses (MERRA2 and ERA5). We showed that stratospheric ozone depletion before the Montreal Protocol introduction and partial recovery after that were chiefly driven by ODS. Stratospheric aerosol from major volcanic eruptions caused only short-term (up to 5 years) ozone decline. Increased greenhouse gas emissions dominate the ongoing long-term stratospheric cooling as well as tropospheric and surface warming. Solar irradiance contributed to short-term fluctuations but had a minimal long-term impact. Furthermore, our analysis of the solar signal in the tropical stratosphere underscores the complex interplay of solar radiation with volcanic, oceanic, and atmospheric factors, revealing significant altitudinal distributions of temperature and ozone responses to solar activity. Our findings advocate further innovative methodologies to take into account the nonlinearity of the atmospheric processes.