Why does the the dielectric constant of a ferroelectric increases with temperature, below $T_C$? 
The above figure is taken from C. Kittel.
When a ferroelectric substance (say, BaTi${\rm O}_3$) at room temperature is gradually heated, the dielectric constant $\varepsilon_r$ first increases and then attains a peak at a temperature called the Curie temperature $T_C$, and above $T_C$, further increase in the temperature causes a rapid decrease in the dielectric constant $\varepsilon_r$. The decrease in $\varepsilon_r$ above $T_C$ can be understood from the ferroelectric to paraelectric transition in which there is a structural phase transition from the tetragonal unit cell structure (carrying a nonzero dipole moment) to the cubic unit cell structure (carrying no nonzero dipole moment).
But what is the reason for the initial growth in the dielectric constant when the temperature is raised from room temperature to $T_C$?
 A: The response of dielectric constants to temperature is model-dependent; thus, I would say that there is no simple rule of thumb. However, in the specific case of phase transitions, the material always builds up long-range correlations between its parts and fluctuations are very intense (near the critical temperature, there is not a well-defined phase of matter, and small perturbations end up with dramatical responses).
For this reason, all the response properties are generally increased. The dielectric constant is one of them, as it is the degree of response of a material to an applied electric field. In summary, the dielectric constant (and other responses to external perturbations) will in general increase towards the critical temperature both ways, as it is a region of extreme fluctuations.
A: This reference may help: . "In a crystalline solid, there are only certain orientations permitted by the lattice. To switch between these different orientations, a molecule must overcome a certain energy barrier ΔE", which requires enough thermal energy. With decreasing temperature, "the orientational mode becomes “frozen out” and can no longer contribute to overall polarisation, leading to a drop in the dielectric constant".
