Six ALAMO floats are deployed within the tropical warm pool of the eastern Indian Ocean, to study the thermal stratification in the diurnal warm layer (DWL) during strong diurnal SST variation (DV SST) prior to the onset of Madden-Julian Oscillations (MJO). Strong DV SST of > 2 °C is measured by four floats before the passage of a MJO event (i.e., during the suppressed phase), when the peak insolation > 1000 W m^-2 and the wind speed < 3 m s^-1. Even after the occurrence of daytime peak SST, the temperature gradient in the DWL can still extend to > 10 m until the midnight, which may be driven by the turbulent mixing at the base of DWL. Interestingly, the foundation SST (SST_fnd) at three floats increases rapidly from 26.4 °C to > 27.6 °C over two days, coincident with the shoaling of surface mixed layer depth (MLD) by more than 20 m. The strongly stratified near surface layer may sustain higher SSTs and enhance air-sea heat fluxes until the onset of stronger winds. The KPP mixing scheme used in a 1-D model can simulate the observed DV SST magnitude reliably, but fail to predict the rapid increase of SST_fnd. The magnitude of DV SST is affected by the near surface stratification, but the SST_fnd is modulated by the evolution of stratification above the MLD. Future field measurements in the upper ocean during diurnal warming are proposed to help improve air-sea flux simulations and the forecast of MJOs.