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Despite increasing empirical evidence of strong links between climate and economic growth, there is no established model to describe the dynamics of how different types of climate shocks affect growth patterns. Here we present the first comprehensive, comparative analysis of the long-term dynamics of one-time, temporary climate shocks on production factors, and factor productivity, respectively, in a Ramsey-type growth model. Damages acting directly on production factors allow us to study dynamic effects on factor allocation, savings and economic growth. We find that the persistence of impacts on economic activity is smallest for climate shocks directly impacting output, and successively increases for direct damages on capital, loss of labor and productivity shocks, related to different responses in savings rates and factor-specific growth. Recurring shocks lead to large welfare effects and long-term growth effects, directly linked to the persistence of individual shocks. Endogenous savings and shock anticipation both have adaptive effects but do not eliminate differences between impact channels or significantly lower the dissipation time. Accounting for endogenous growth mechanisms increases the effects. We also find strong effects on income shares, important for distributional implications. This work fosters conceptual understanding of impact dynamics in growth models, opening options for links to empirics.