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In water-deficient areas, water resource management requires evapotranspiration at high spatiotemporal resolution - an impossible situation given the trade-off between spatial and temporal resolutions in space-borne systems. Some researchers have suggested sharpening the Moderate Resolution Imaging Spectroradiometer (MODIS) land-surface temperature product with a resolution from 1 km to 250m and a functional relationship between surface temperature (Tr) and normalized difference vegetation index (NDVI). Evapotranspiration at 250m resolution can be obtained once every few days using this technique. Based on the interpretation of the triangular Tr-NDVI space and assuming uniform soil moisture conditions in a coarse pixel, this paper suggests an alternative algorithm - the triangle algorithm - for sharpening. The triangle algorithm was tested using Landsat 7 Enhanced Thematic Mapper Plus (ETM+) data from an arid zone. Sharpened surface temperatures and reference temperatures were compared at 60m and 240m resolutions. Root mean square errors with the triangle algorithm are smaller than those with a functional relationship between Tr and NDVI. This paper will also discuss the impact of soil moisture variations in the coarse pixel on the triangle algorithm. Finally we should mention that the triangle algorithm only applies to regions with non-stressed vegetation canopies.