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In this letter, a general Bayesian data fusion (BDF) approach is proposed and applied to the spatial enhancement of ASTER thermal images. This method fuses information coming from the visible or near-infrared bands (15 times 15 m pixels) with the thermal infrared bands (90 times 90 m pixels) by explicitly accounting for the change of support. By relying on linear multivariate regression assumptions, differences of support size for input images can be explicitly accounted for. Due to the use of locally varying variances, it also avoids producing artifacts on the fused images. Based on a set of ASTER images over the region of Lausanne, Switzerland, the advantages of this support-based approach are assessed and compared to the downscaling cokriging approach recently proposed in the literature. Results show that improvements are substantial with respect to both visual and quantitative criteria. Although the method is illustrated here with a specific case study, it is versatile enough to be applied to the spatial enhancement problem in general. It thus opens new avenues in the context of remotely sensed images.