We construct an endogenous (Bayesian) learning model with fat-tailed uncertainty on the equilibrium climate sensitivity and solve the model with stochastic dynamic programming. In our model a decision maker updates her belief on the climate sensitivity through temperature observations each time period and takes a course of action (carbon reductions) based on her belief. We find that the uncertainty is partially resolved over time, although the rate of learning is relatively slow, and the decision maker with a possibility of learning lowers the efforts to reduce carbon emissions relative to the no-learning case. The larger the tail effect, the larger the counteracting learning effect. Learning at least partly offsets the tail-effect of deep uncertainty. This is intuitive in that the decision maker fully utilizes the information revealed to reduce uncertainty, and thus she can make a decision contingent on the updated information. In addition, with various scenarios, we find that learning enables the economic agent to have less regrets for her past actions after the true value of the uncertain variable turns out to be different from the initial best guess. Furthermore the optimal decisions in the learning case are less sensitive to the true value of the uncertain variable than the decisions in the uncertainty case. The reason is that learning lets uncertainty converge to the true value of the state in the sense that the variance approaches 0 as information accumulates.