Satellite land surface temperature (Ts) provides valuable information on vegetation drought stress via its physical linkage to plant stomatal activity and transpiration. New-generation geostationary satellites offer opportunities to monitor sub-diurnal variations in Ts and thus track plant physiological stress response occurring at sub-daily timescales. Nevertheless, the potential of satellite Ts and its derived metrics for early detection of vegetation drought stress before visible canopy changes occur has not been widely assessed. Here, we developed a parsimonious Surface-Air Temperature Difference Anomaly (SATDA) method for tracking vegetation drought stress using the cumulative sub-diurnal difference from late-morning to early-afternoon between Ts from the Himawari8 geostationary satellite and hourly air temperature (Ta) from meteorological grids. SATDA utilised Ts - Ta as the physical driving gradient for sensible heat flux (H) to capture anomalous sensible heating due to reduced plant transpiration. We used SATDA to monitor the spatio-temporal patterns of the 2017-2019 Tinderbox Drought in southeast Australia. We benchmarked the skill of SATDA in forecasting visible drought-induced vegetation greenness decline against both conventional water availability-based indices (i.e., precipitation and soil moisture anomalies) and existing satellite Ts indices (i.e., Temperature Condition Index and Temperature Rise Index) across diverse climates and land covers. SATDA effectively captured a rapidly intensifying flash drought event at multi-week timescales (Jul to Sep 2019) embedded within the multi-year Tinderbox Drought, which contributed to detrimental impacts on agricultural production and increased wildfire risk. SATDA showed the best vegetation greenness forecast skill in the transitional semi-arid and sub-humid climates, with forecast correlation >0.5 at 32-day lead time. The advantage over water availability-based indices was more evident in woody-dominated ecosystems than herbaceous-dominated ecosystems, likely due to the importance of physiological regulations by trees during droughts such as deeper roots and stronger stomatal control. SATDA, based on Ts - Ta, showed overall better vegetation greenness forecasts than two Ts-only indices, especially in woody vegetation. Finally, SATDA showed consistently greater advantage over water availability-based and Ts-only indices in forecasting visible vegetation decline as the drought intensity increased. The parsimonious process-based SATDA method suits global-scale operational implementation to complement vegetation drought monitoring and early warning systems.