This paper addresses the problem of meeting a predetermined temperature target cost-effectively under uncertainty and gradual learning on climate sensitivity. The firstorder optimality conditions to a stochastic cost-minimization problem with a temperature constraint are first provided, portraying how marginal costs evolve with an optimal hedging strategy. Then, numerical stochastic scenarios with cost curves fitted to recent climate changemitigation scenarios are presented, illustrating both the range of possible future pathways and the effect of uncertainty to the solution. Last, the effect of several different sets of assumptions on the optimal hedging strategy are analyzed. The results highlight that the hedging of climate sensitivity risk calls for deeper early reductions, although the possibility of different assumptions prevents providing accurate policy guidance.