  Effects of Pauli paramagnetism on thermodynamic quantities in a vortex state,
such as the specific heat $C$ and magnetization $M$, are studied using the
quasiclassical Eilenberger formalism. We demonstrate that with an increase of
paramagnetic depairing effect, the sigh of the curvature of the field
dependence of $C$ changes from negative to positive, and that the Maki
parameter $\kappa_2$ becomes an increasing function of temperature. Our results
provide a natural explanation for the unusual field dependence of $C$ seen in
CeCoIn$_5$ in terms of the paramagnetic effect.
