  We study the thermodynamics and the susceptibilities of quark matter in the
framework of two-flavor Nambu-Jona-Lasinio model at finite isospin chemical
potential and temperature. Isospin number density, normalized energy density
and trace anomaly are shown to be in good agreement with the available lattice
data as well as with the results from chiral perturbation theory at zero
temperature. We also study how susceptibilities depend on the isospin chemical
potential and on temperature. We find a peak for the chiral, pion, and isospin
susceptibilities at the critical isospin chemical potential, $\mu_I^c(T)$, at
the boundary of the phase transition between the normal and pion superfluid
phase. Moreover, temperature makes the transition from normal to pion condended
phase smoother. We also note that the pion susceptibility always remains zero
in the normal phase while it is finite in the superfluid phase.
