  We show how the quasiparticle picture of quarks changes near but above the
critical temperature T_c of the color-superconducting phase transition in the
heated quark matter. We demonstrate that a non-Fermi liquid behavior of the
matter develops drastically when the diquark coupling constant is increased
owing to the coupling of the quark with the pairing soft mode: We clarify that
the depression and eventually the appearance of a gap structure in the spectral
function as well as the anomalous quark dispersion relation of the quark can be
understood in terms of the resonant scattering between the incident quark and a
particle near the Fermi surface to make the pairing soft mode.
