This paper studies the role of demand uncertainty in temporal discrimination when the retailer applies markdown pricing facing strategic customers. We consider a model in which a retail firm announces a pair of declining prices for two selling periods, and customers with heterogeneous valuations each decide whether to buy a unit early, later or never. In this model, if the demand function is linear and its parameters are common knowledge, there never exist any markdown prices that achieve temporal discrimination for any feasible model parameters. Either all buying customers wait, or all buy early. By contrast, if the demand level is unknown, there always exists a temporally discriminating markdown pricing scheme for all feasible model parameters. We derive qualitative insights to the way demand uncertainty and Bayesian updating contribute to temporal discrimination, which broadly apply to nonlinear demand functions as well. We also show that in case of demand uncertainty, there always exists a temporally discriminating pricing scheme that yields a strictly higher profit to the retailer than the optimal static pricing scheme. Ironically, however, the retailer cannot implement the optimal scheme due to the same demand uncertainty.