Earlier studies suggest that the mixed-layer (ML) temperature or sea surface temperature (SST) of the Bay of Bengal during the summer monsoon is determined primarily by air–sea fluxes. We use an oceanic general circulation model (OGCM) to show that oceanic processes also play a significant role. Model heat-budget computations show that horizontal and vertical advection, constituting the direct role of dynamics, contribute significantly to the SST tendency in the western bay. The eastern limit of this direct-role regime is determined by downwelling Rossby waves, which are forced largely from the equatorial Indian Ocean, but are modified by alongshore winds at the eastern boundary and Ekman pumping along their westward path across the bay. The current and, as a result, advection weaken behind the Rossby waves. To the east of the Rossby wavefront, the thermocline is deep, permitting a deeper ML, but the actual ML depth (MLD) depends on the wind speed, with salinity also playing a role in the northern bay. Yet, there is negligible change in the SST even when MLD changes significantly because the deep thermocline decouples the changes in MLD and SST. In contrast, the shallower thermocline in the western bay limits the potential MLD, leading to larger changes in SST. The upwelling (downwelling) Rossby wave essentially conditions the upper ocean by decreasing (increasing) the potential depth of the mixed layer. SST variation weakens only when the thermocline deepens during downwelling events, which occur later in the western bay because Rossby waves propagate westward. The significant, but subtle, role of the Rossby waves in decoupling the changes in MLD and SST via downwelling is indirect, unlike the direct role of advection estimated in a standard heat-budget computation, and has been largely ignored in earlier studies.