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The scientific and wider interest in the relationship between atmospheric temperature (T) and concentration of carbon dioxide ([CO2]) has been enormous. According to the commonly assumed causality link, increased [CO2] causes a rise in T. However, recent developments cast doubts on this assumption by showing that this relationship is of the hen-or-egg type, or even unidirectional but opposite in direction to the commonly assumed one. These developments include an advanced theoretical framework for testing causality based on the stochastic evaluation of a potentially causal link between two processes via the notion of the impulse response function. Using, on the one hand, this framework and further expanding it and, on the other hand, the longest available modern time series of globally averaged T and [CO2], we shed light on the potential causality between these two processes. All evidence resulting from the analyses suggests a unidirectional, potentially causal link with T as the cause and [CO2] as the effect. That link is not represented in climate models, whose outputs are also examined using the same framework, resulting in a link opposite the one found when the real measurements are used.