We have investigated the mixing phenomena in a stratified two-layer fluid system where a layer of fresh water is initially put on top of salty water. When this stabilized system by a salt gradient is heated from below, it becomes unstable by an onset of convection in the lower layer due to the thermal buoyancy effect. Thereafter the heat and salt is ready to diffuse into the upper layer through the adjacent diffusive interface. To examine quantitatively the merging process of the two layers as the destabilizing temperature gradient gets more dominant, we have measured many profiles of temperature and salinity in both layers by using accurate micro-scale measurement probes. Each run of experiment with several different initial concentrations of salt is followed until there appears a sudden overturning into a perfect mixing state. The order of thermal Rayleigh number has been kept as order of 107 around which we have observed uniform temperature and salt profiles in the upper layer without any external mixing force. Since the employed measuring probes shows good reproducibility and very fast response time to the variations of the temperature and salt concentration, the mixing phenomena with the double-diffusive convection has been pursued easily.