High-resolution atmospheric data is essential for understanding local atmospheric processes, however it is computationally expensive to achieve such high resolutions through physical models. Recently, deep learning techniques, particularly those used in Single Image Super-Resolution, have emerged as a promising approach for statistical downscaling. However, much of the existing research has focused on enhancing model performance within small geographical regions, with limited attention given to the transferability of these models to diverse areas outside of their training domain. This paper introduces a methodology that evaluates the ability of a UNet model to downscale daily 2-meter temperature data outside its training region. The proposed approach uses one-third of the Contiguous United States to train the model, and assesses its performance on unseen areas. Our experimental design deliberately tests both spatial and temporal generalization, demonstrating that relatively compact models can effectively transfer downscaling capabilities to new regions. This results in improvements across key performance metrics including Mean Absolute Error, Root Mean Square Error, and Peak Signal-to-Noise Ratio. Additionally, our approach significantly reduces computational costs while improving downscaling accuracy across diverse climatic and topographic conditions.