Providing reliable information on climate change at local scale remains a challenge of first importance for impact studies and policymakers. Here, we propose a novel hybrid downscaling method combining the strengths of both empirical statistical downscaling methods and Regional Climate Models (RCMs). In the longer term, the final aim of this tool is to enlarge the high-resolution RCM simulation ensembles at low cost to explore better the various sources of projection uncertainty at local scale. Using a neural network, we build a statistical RCM-emulator by estimating the downscaling function included in the RCM. This framework allows us to learn the relationship between large-scale predictors and a local surface variable of interest over the RCM domain in present and future climate. The RCM-emulator developed in this study is trained to produce daily maps of the near-surface temperature at the RCM resolution (12 km). The emulator demonstrates an excellent ability to reproduce the complex spatial structure and daily variability simulated by the RCM, particularly how the RCM refines the low-resolution climate patterns. Training in future climate appears to be a key feature of our emulator. Moreover, there is a substantial computational benefit of running the emulator rather than the RCM, since training the emulator takes about 2 h on GPU, and the prediction takes less than a minute. However, further work is needed to improve the reproduction of some temperature extremes, the climate change intensity and extend the proposed methodology to different regions, GCMs, RCMs, and variables of interest.