Climate downscaling is a way to turn coarse climate data into high-resolution information, which is crucial for making policies and preparing for climate change. There are two main methods: dynamical and statistical. The dynamical method uses complex physics-based models, called Regional Climate Models (RCMs), which simulate climate processes in specific regions. These models are accurate but require a lot of computing power and can still introduce some errors. The statistical method, on the other hand, uses data-driven models like deep learning to learn the relationship between low- and high-resolution data. This approach is much faster and less costly, but it can struggle when used to predict future climates, because it is trained on past observations. To fix this, we use a technique called domain adaptation, which helps the model learn from past data in a way that makes it better at predicting future conditions. Our experiments show that this adapted model performs better than non-adapted baselines when tested under future climate scenarios.