  We explore the quark properties at finite temperature near but above the
critical temperature of the chiral phase transition. We investigate the effects
of the precursory soft mode of the phase transition on the quark dispersion
relation and the spectral function. It is found that there appear novel
excitation spectra of quasi-quarks and quasi-antiquarks with a three-peak
structure, which are not attributed to the hard-thermal-loop approximation. We
show that the new spectra originate from the mixing between a quark
(anti-quark) and an anti-quark hole (quark hole) caused by a ``resonant
scattering'' of the quasi-fermions with the thermally-excited soft mode which
has a small but finite excitation energy.
