  A rigorous three-dimensional relativistic equation for quark-antiquark bound
states at finite temperature is derived from the thermal QCD generating
functional which is formulated in the coherent-state representation. The
generating functional is derived newly and given a correct path-integral
expression. The perturbative expansion of the generating functional is
specifically given by means of the stationary-phase method. Especially, the
interaction kernel in the three-dimensional equation is derived by virtue of
the equations of motion satisfied by some quark-antiquark Green functions and
given in a closed form which is expressed in terms of only a few types of Green
functions. This kernel is much suitable to use for exploring the deconfinement
of quarks. To demonstrate the applicability of the equation derived, the
one-gluon exchange kernel is derived and described in detail.
