Deep learning models have shown great promise in diverse remote sensing applications. However, they often struggle to generalize across geographic regions unseen during training due to domain shifts. Domain shifts occur when data distributions differ between the training region and new target regions, due to variations in land cover, climate, and environmental conditions. Test-time adaptation (TTA) has emerged as a solution to such shifts, but existing methods are primarily designed for classification and are not directly applicable to regression tasks. In this work, we address the regression task of spatio-temporal fusion (STF) for land surface temperature estimation. We propose an uncertainty-aware TTA framework that updates only the fusion module of a pre-trained STF model, guided by epistemic uncertainty, land use and land cover consistency, and bias correction, without requiring source data or labeled target samples. Experiments on four target regions with diverse climates, namely Rome in Italy, Cairo in Egypt, Madrid in Spain, and Montpellier in France, show consistent improvements in RMSE and MAE for a pre-trained model in Orléans, France. The average gains are 24.2% and 27.9%, respectively, even with limited unlabeled target data and only 10 TTA epochs.