A strong positive Indian Ocean Dipole (pIOD) induces weather extremes such as the 2019 Australian bushfires and African floods. The impact is influenced by sea surface temperature (SST), yet models disagree on how pIOD SST may respond to greenhouse warming. Here we find increased SST variability of strong pIOD events, with strong equatorial eastern Indian Ocean cool anomalies, but decreased variability of moderate pIOD events, dominated by western warm anomalies. This opposite response is detected in the Coupled Model Inter-comparison Project (CMIP5 and CMIP6) climate models that simulate the two pIOD regimes. Under greenhouse warming, the lower troposphere warms faster than the surface, limiting Ekman pumping that drives the moderate pIOD warm anomalies; however, faster surface warming in the equatorial western region favours atmospheric convection in the west, strengthening equatorial nonlinear advection that forces the strong pIOD cool anomalies. Climate extremes seen in 2019 are therefore likely to occur more frequently under greenhouse warming. The strength of a positive Indian Ocean Dipole (pIOD) is set by sea surface temperature gradient across the equatorial Indian Ocean. Modelling shows warming will increase strong pIODs but decrease moderate pIODs, as faster surface warming in the west sets up conducive conditions for the strong events.