The application of a method is shown here for obtaining LST images with enhanced spatial resolution using the LST at a coarser resolution and the Normalized Difference Vegetation Index (NDVI) of the same scene using Downscaling Cokriging (DCK). A LST image with perfect coherence was obtained by applying this method to a Landsat 7 ETM+ image. This implies that, if the downscaled LST image is degraded to its original resolution, the degraded image obtained is identical to the original. Hence high spatial resolution LST images were obtained without altering the original radiometry with the inclusion of artefacts. Moreover, the performance of DCK was compared with global and local TSHARP methods. The RMSE of the sharpened images were 0.85, 0.92 and 1.1 K, respectively.