  The thermodynamics of hydration changes gradually from entropic for small
solutes to enthalpic for large ones. The small-to-large crossover lengthscale
of hydrophobic hydration depends on the thermodynamic conditions of the solvent
such as temperature, pressure, presence of additives, etc... We attempt to shed
some light on the temperature dependence of the crossover lengthscale by using
a probabilistic approach to water hydrogen bonding that allows one to obtain an
analytic expression for the number of bonds per water molecule as a function of
both its distance to a solute and solute radius. Incorporating that approach
into the density functional theory, one can examine the solute size effects on
its hydration over the entire small-to-large lengthscale range at different
temperatures. Knowing the dependence of the hydration free energy on
temperature and solute size, one can obtain its enthalpic and entropic
contributions as functions of temperature and solute size. These function can
provide interesting insight into the temperature dependence of the crossover
lengthscale of hydrophobic hydration. The model was applied to the hydration of
spherical particles of various radii in water in the temperature range from
T=293.15 K to T=333.15 K. The model predictions for the temperature dependence
of the hydration free energy of small hydrophobes are consistent with the
experimental and simulational data. Three alternative definitions for the
small-to-large crossover length-scale of hydrophobic hydration are proposed,
and their temperature dependence is obtained. Depending on the definition and
temperature, the small-to-large crossover in the hydration mechanism is
predicted to occur for hydrophobes of radii from one to several nanometers.
Independent of its definition, the crossover length-scale is predicted to
decrease with increasing temperature.
