  We study the quantum paraelectric-ferroelectric transition near a quantum
critical point, emphasizing the role of temperature as a "finite size effect"
in time. The influence of temperature near quantum criticality may thus be
likened to a temporal Casimir effect. The resulting finite-size scaling
approach yields $\frac{1}{T^2}$ behavior of the paraelectric susceptibility
($\chi$) and the scaling form $\chi(\omega,T) = \frac{1}{\omega^2}
F(\frac{\omega}{T})$, recovering results previously found by more technical
methods. We use a Gaussian theory to illustrate how these
temperature-dependences emerge from a microscopic approach; we characterize the
classical-quantum crossover in $\chi$, and the resulting phase diagram is
presented. We also show that coupling to an acoustic phonon at low temperatures
($T$) is relevant and influences the transition line, possibly resulting in a
reentrant quantum ferroelectric phase. Observable consequences of our approach
for measurements on specific paraelectric materials at low temperatures are
discussed.
