What is the long-run effect of climate change on how income is distributed between capital and labor? To answer this question, we develop an equilibrium growth model with labor- and capital-augmenting productivities that are affected by changes in temperature. We show that how temperature affects the long-run division of income only depends on the elasticity of substitution between labor and capital and how temperature affects capital-augmenting productivity. Labor-augmenting productivity and the elasticity of labor supply play no role in temperature's long-run effects on factor shares.
Liu et al. (Fri,) studied this question.