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.