Economists have analyzed potential for damages from climate change from theoretical analyses and with Integrated Assessment Models (IAMs). Analytical models typically write damages as a function of the carbon stock, while IAMs typically view damages as based on temperatures. In this paper, we evaluate the implications for adapting analytic models to include two state variables—temperature and carbon stocks. We first provide an analytical comparison of a model where damages are based on carbon stocks against a model where damages are based on temperatures. When damages are based on carbon stocks, the time path of optimal emissions is described by a first-order differential equation; when damages are based on temperatures, the time path of optimal emissions is described by a second-order differential equation. We then proceed to an empirical analysis of the link between temperatures and carbon stocks. Our empirical analysis strongly supports a relation between levels of carbon stocks and changes in temperatures, and indicates the virtual absence of a linkage between levels of carbon and levels of temperature. As such, it is broadly supportive of a more elaborate modeling structure, under which two state variables are included in the analytical framework.