  We report on an analysis of the quark spectral representation at finite
temperatures based on the quark propagator determined from its Dyson-Schwinger
equation in Landau gauge. In Euclidean space we achieve nice agreement with
recent results from quenched lattice QCD. We find different analytical
properties of the quark propagator below and above the deconfinement
transition. Using a variety of ansaetze for the spectral function we then
analyze the possible quasiparticle spectrum, in particular its quark mass and
momentum dependence in the high temperature phase. This analysis is completed
by an application of the Maximum Entropy Method, in principle allowing for any
positive semi-definite spectral function. Our results motivate a more direct
determination of the spectral function in the framework of Dyson-Schwinger
equations.
