  We prove the existence of correlations between the equilibrium states at
different temperatures of the multi-$p$-spin spherical spin-glass models with
continuous replica symmetry breaking: there is no chaos in temperature in these
models. Furthermore, the overlaps satisfy ultrametric relations. As a
consequence the Parisi tree is essentially the same at all temperatures with
lower branches developing when lowering the temperature. We conjecture that the
reference free energies of the clusters are also fixed at all temperatures as
in the generalized random-energy model.
