Recent laboratory studies indicate that the hydrated form of crystalline NaCl is potentially important for atmospheric processes involving depositional ice nucleation on NaCl dihydrate particles under cirrus cloud conditions. However, recent experimental studies reported a strong discrepancy between the temperature intervals where the efflorescence of NaCl dihydrate has been observed. Here we report the measurements of the volume specific nucleation rate of crystalline NaCl in the aqueous solution droplets of pure NaCl suspended in an electrodynamic balance at constant temperature and humidity in the range from 250 K to 241 K. Based on these measurements, we derive the interfacial energy of crystalline NaCl dihydrate in a supersaturated NaCl solution and determined its temperature dependence. Taking into account both temperature and concentration dependence of nucleation rate coefficients, we explain the difference in the observed fractions of NaCl dihydrate reported in the previous studies. Applying the heterogeneous classical nucleation theory model, we have been able to reproduce the 5 K shift of the NaCl dihydrate efflorescence curve observed for the sea salt aerosol particles, assuming the presence of super-micron solid inclusions (hypothetically gypsum or hemihydrate of CaSO4). These results support the notion that the phase transitions in microscopic droplets of supersaturated solution should be interpreted by accounting for the stochastic nature of homogeneous and heterogeneous nucleation and cannot be understood on the ground of bulk phase diagrams alone.