  We discuss the calculation of the linear conductance through a
Coulomb-blockade quantum dot in the presence of interactions beyond the
charging energy. In the limit where the temperature is large compared with a
typical tunneling width, we use a rate-equations approach to describe the
transitions between the corresponding many-body states. We discuss both the
elastic and rapid-thermalization limits, where the rate of inelastic scattering
in the dot is either small or large compared with the elastic transition rate,
respectively. In the elastic limit, we find several cases where a closed
solution for the conductance is possible, including the case of a constant
exchange interaction. In the rapid-thermalization limit, a closed solution is
possible in the general case. We show that the corresponding expressions for
the linear conductance simplify for a Hamiltonian that is invariant under spin
rotations.
