Despite recent challenges, conventional wisdom has held that heating over the Tibetan Plateau leads to increased Indian summer monsoon rainfall via enhancement of cross-equatorial circulation aloft, and a concurrent strengthening of both the Somali Jet and westerly winds that bring moisture to southern India. We show that such heating, quantified by monthly estimates of moist static energy in the atmosphere just above the surface, correlates with summer monsoon rainfall, but only in the early (20 May to 15 June) and late (September 1 to 15 October) monsoon season. Correlations during the main monsoon season (15 June to 31 August) are small and insignificant. The positive correlations with early and late monsoon season, however, allow for heating over Tibet to modulate as much as ~30% of the total rainfall. Furthermore, we demonstrate that heating over Tibet is independent of the El Niño Southern Oscillation, so that together they explain a substantial portion of variability in the early and late season rainfall, providing potential predictability. These links may also explain the wet conditions over India during early Holocene time and provide a quantitative link between a rise of Tibet and stronger Somali Jet.