The Bay of Bengal has a complex upper-ocean temperature and salinity structure that is, in places, characterized by strong salinity stratification and multiple inversions in temperature. Here, two short time series from continuously profiling floats, equipped with microstructure sensors to measure subsurface mixing, are used to highlight implications of complex hydrography on upper-ocean heat content and the evolution of sea surface temperature. Weak mixing coupled with the existence of subsurface warm layers suggest the potential for storage of heat below the surface mixed layer over relatively long time scales. On the diurnal time scale, these data demonstrate the competing effects of surface heat flux and subsurface mixing in the presence of thin salinity-stratified mixed layers with temperature inversions. Pre-existing stratification can amplify the sea surface temperature response through control on the vertical extent of heating and cooling by surface fluxes. In contrast, subsurface mixing entrains relatively cool water during the day and relatively warm water during the night, damping the response to daytime heating and nighttime cooling at the surface. These observations hint at the challenges involved in improving monsoon prediction at longer, intraseasonal time scales as models may need to resolve upper-ocean variability over short time and fine vertical scales.