This review summarises the data available in the literature. It also includes the authors' published results of precision densimetric measurements. The research concerns with the physically unusual phenomenon of "thermally activated isobaric partial densification of the structure" (TIPCS) of dissolved water, or its so-called "negative partial molar expandability" (NPEA) in several organic solvents. They contain amphiproton hydroxyl-containing media of three alcohols: methyl alcohol (MA), tertiary butyl alcohol (TBAlcohol), and amyl or pentyl alcohol (TPA), so asprotophilic media of two amines: tert butylamine (TBAmine) and ethylenediamine (EDA). The discussed TIPCS phenomenon, associated with a decrease in the standard (partial at infinite dilution) volume of solvated water with increasing temperature, was discovered about half a century ago in alkanol solutions of H2O and recently - in water-containing media of alkylamines. However, nowadays this extraordinary effect has not yet found its physically based interpretation. It allows ones to predict the possibility of TIPCS occurrence in the binary liquid-phase system specifically selected for the study. Our comprehensive data analysis allowed us to make several inferences regarding the main characteristics of a standard solution of H2O in an organic solvent. They cause extraordinary changes in the volume of the formed solvatocomplex of water under the influence of increasing temperature. Firstly, the energy parameters of the intermolecular interaction (relative affinity) water solvent noticeably dominate over those of the solvent-solvent interaction. Those differences become more evident with increasing temperature. Secondly, a higher rate of thermal expansion of the organic solvent structure in volume (inbulk) is found than influence of temperature on structural packing of the resulting mixed molecular aggregate or water solvates complex. Thirdly, the difference in the parameters of water-solvent and solvent-solvent interactions depends not only on the proton-donor/acceptor properties of the molecules contacting in solution, but also on the configuration of the structural packing of the solvating medium. It determines the nature of steric hindrances to the formation of H-bonds. Therefore, the absolute values of the mentioned parameters of relative affinity at 298.15 K increase in the series: MA << EDA ≈ TBAmine < TPAlcohol < TBAmine. It can indicate a relative strengthening of the specific interaction (mainly through the formation of hydrogen bonds) between the molecules of water and amphiprotonic or protophilic solvent in the above sequence. Indeed, difference in the solvent-solvent and water-solvent hydrogen bonding energies in the discussed liquid media of alkylamines (TBAmine and EDA) and tertiary isomeric alkanols (TBAlcohol and TPA) - with the most evident basicity - turned out to be noticeably larger than in the structural packing of water methanol solution. The ability of the components to specific interactions is quite comparable in those compounds.