  While the Gibbs states of spin glass models have been noted to have an
erratic dependence on temperature, one may expect the mean over the disorder to
produce a continuously varying ``quenched state''. The assumption of such
continuity in temperature implies that in the infinite volume limit the state
is stable under a class of deformations of the Gibbs measure. The condition is
satisfied by the Parisi Ansatz, along with an even broader stationarity
property. The stability conditions have equivalent expressions as marginal
additivity of the quenched free energy. Implications of the continuity
assumption include constraints on the overlap distribution, which are expressed
as the vanishing of the expectation value for an infinite collection of
multi-overlap polynomials. The polynomials can be computed with the aid of a
"real"-replica calculation in which the number of replicas is taken to zero.
