The key element in the tension between those who believe climate change is an issue and those who do not is essentially the question of whether we are merely in a long period of shock-induced above average temperatures or if we have led to this increase in temperatures by anthropogenic carbon emissions. The model proposed in this paper allows for a model in which we weigh observations on temperature against the potential that these are generated by a combination of uncertain parameters; namely the coefficient of autoregression and the sensitivity of temperature change to atmospheric carbon levels. This paper shows that, contrary to predictions in the literature that we can resolve uncertainty very quickly, the time to learn may be on the order of thousands of years when uncertainty surrounds two parameters in the law of motion for temperature. When the learning model is embedded in an optimal policy growth model, policy decisions are found to be affected by the prior mean but not the variance. A new solution algorithm which relies on randomization and least squares approximation is applied to solve the value function in the model.