  Chiral quark models with non-local covariant separable interactions at finite
temperature and chemical potential are investigated. We develop a formalism in
which the different quark properties are evaluated taking into account the
analytic structure of the quark propagator. In this framework we study the
chiral restoration phase transition for several definite non-local regulators,
including that arising within the instanton liquid picture. We find that in all
cases the chiral transition is of first order for low values of T, turning into
a smooth crossover at a certain "end point". Using model parameters which lead
to the physical pion mass and decay constant, we find for the position of this
"end point" the values (T_E, mu_E) approx. (60-70, 180-210) MeV. We also
discuss the special relevance of the first poles of the quark propagator.
