  The temperature and transverse field dependence of the entropy and the
specific heat of ferroics in the quantum paramagnetic (QPa) state is
investigated using the transverse Ising model (TIM) with different spin values
within mean field and Gaussian spin fluctuation approximations. A maximum peak
of the temperature dependence of the specific heat curves is enhanced in the
QPa state due to spin fluctuations. This peak shifts to higher temperature
region and its magnitude reduces with increasing transverse field. In addition,
the temperature corresponding to this maximum depends linearly on the deviation
of the transverse field from its critical value. The obtained specific heat
qualitatively agrees with the experimental observation for the
quasi-one-dimensional (1D) Ising ferromagnet CoNb$_2$O$_6$ in the QPa phase. It
is also shown that the spin-1/2 three dimensional (3D) TIM clearly describes
the specific heat of CoNb$_2$O$_6$ in the QPa states near the critical
temperature. However, the spin-3/2 3D-TIM is more adequate than the spin-1/2
3D-TIM for describing the thermal behavior of CoNb$_2$O$_6$ in the QPa states
at high fields and at elevated temperatures.
