  We revisit the metastability properties of the mixed p-spin spherical
disordered models. Firstly, using known methods, we show that there is
temperature chaos in a broad range of temperatures. Secondly, we modify the
definition of the Thouless-Anderson-Palmer free energy density by including
constraints that enforce a chosen overlap between the searched metastable
states and another reference state, that could be a characteristic one of a
different temperature. We argue that this refined analysis provides clues to
understand the weird behaviour of the low temperature relaxation dynamics of
these models, and suggests ways to improve the treatment of the initial
conditions to overcome the difficulties encountered so far.
