Negative sea surface temperature (SST) anomalies associated with positive Indian Ocean Dipole (pIOD) events first appear in the seasonal upwelling zone along the southern coast of Java during May–July. The evolution of anomalous SSTs in this coastal region is analyzed by computing a temperature budget using output from a strongly eddy‐active ocean general circulation model. The seasonal cooling south of Java in May–July is driven by a reduction in incoming shortwave radiation and by vertical mixing, consistent with earlier studies in the region; however, the model budget also shows an advective contribution that drives anomalous cooling at the onset of pIOD events. To identify which process(es) are responsible for the anomalous advective cooling during pIOD events, a novel process index regression method is used to estimate the contributions of wind stress, equatorial Kelvin waves, mesoscale eddies, and Lombok Strait flow to anomalous cooling south of Java. Using this method, wind stress forcing along the west coast of Sumatra is found to make the most substantial contribution to anomalous cooling south of Java, with lesser contributions from equatorially sourced Kelvin waves and local wind stress. Mesoscale eddies redistribute heat from the Lombok Strait outflow, and have an anomalous warming effect on the eastern side of the upwelling region. The process‐specific temperature budget south of Java highlights the importance of wind stress forcing west of Sumatra relative to equatorial and local forcing, and explains most of the mixed layer temperature anomaly evolution associated with advection during pIOD events.