CO2 absorbs and emits radiation, which allows it to act both as radiative forcing and feedback. Recent work has shown CO2’s feedback effect becomes dominant in hothouse climates, giving rise to a non‐monotonic climate sensitivity around 310 K. However, CO2’s feedback effect in colder climates is less clear. We use a line‐by‐line model to explore the CO2‐dependence of the longwave clear‐sky feedback and identify a dividing temperature. Above 290 K, feedback increases with CO2 concentration; below 290 K, feedback decreases with CO2 concentration. We explain this dependence in terms of spectral competition under CO2 increases. In hot climates, CO2’s moderate feedback replaces near‐zero feedback from the H2O bands; in cold climates, CO2’s moderate feedback replaces the large feedback from the surface. Given that global mean temperature is currently close to 290 K, our results suggest that feedback CO2‐dependence is weak at present but can be important in past and future climates.