  We prove chaos in temperature for even $p$-spin models which include
sufficiently many $p$-spin interaction terms. Our approach is based on a new
invariance property for coupled asymptotic Gibbs measures, similar in spirit to
the invariance property that appeared in the proof of ultrametricity in
arXiv:1112.1003, used in combination with Talagrand's analogue of Guerra's
replica symmetry breaking bound for coupled systems.
