We study the quark propagator at finite temperature through
non-perturbative solution of a truncated Scwhinger-Dyson (SD) equation for
the quark self-energy. The truncation used ignores the coupling to the
gluon and ghost self-energy equations by modelin g the gluon propagator.
We study several different Ans\"{a}tze for the gluon propagator which
allow us to study both strongly coupled QED and QCD. To model confinement
within QCD the gluon propagator is chosen to be a sum of a delta function,
which mode ls the strong infrared enchancement expected in the gluon
propagator, and a perturbative piece, which models the short range
aspects. It is shown that this model can describe both the deconfinement
and chiral symmetry phase transitions and provides insig ht into the
relation between them. In solving the SD equation we have gone beyond the
bare vertex approximation by applying the finite temperature
Ward-Takahashi identity allowing us to write the finite temperature
quark-gluon vertex function in terms of the finite temperature quark
propagator. It is shown that vertex improvement restores gauge invariance
of the results. Numerical solution of the SD equation shows that at low
temperature the quark propagator does not contain any poles on the real
$\vl{ p}^2$ axis, instead having a pair of timelike complex conjugate
poles. The imaginary part of the position of these poles is suggested to
be related to the rapid decay of the quark propagator due to dynamical
pair generation. We find that at a critical t emperature, $T_c^{\rm dc}$,
these complex conjugate poles combine into a single pole on the real
timelike $\vl{p}^2$ axis signaling quark deconfinement. In addition, we
demonstrate that the chiral and deconfinement phase transitions are
coincident in the limit of vanishing bare quark mass. For finite bare
quark mass we find that the chiral transition occurs prior to the
deconfinement transition, with the separation between the two being on the
order of the bare quark mass.