In applications of climate information, coarse-resolution climate projections commonly need to be downscaled to a finer grid. One challenge of this requirement is the modeling of subgrid variability and the spatial and temporal dependence at the finer scale. Here, a postprocessing procedure for temperature projections is proposed that addresses this challenge. The procedure employs statistical bias correction and stochastic downscaling in two steps. In the first step, errors that are related to spatial and temporal features of the first two moments of the temperature distribution at model scale are identified and corrected. Second, residual space–time dependence at the finer scale is analyzed using a statistical model, from which realizations are generated and then combined with an appropriate climate change signal to form the downscaled projection fields. Using a high-resolution observational gridded data product, the proposed approach is applied in a case study in which projections of two regional climate models from the Coordinated Downscaling Experiment–European Domain (EURO-CORDEX) ensemble are bias corrected and downscaled to a 1 km × 1 km grid in the Trøndelag area of Norway. A cross-validation study shows that the proposed procedure generates results that better reflect the marginal distributional properties of the data product and have better consistency in space and time when compared with empirical quantile mapping.