  Temperature chaos is an extreme sensitivity of the equilibrium state to a
change of temperature. It arises in several disordered systems that are
described by the so called scaling theory of spin glasses, while it seems to be
absent in mean field models. We consider a model spin glass on a tree and show
that although it has mean field behavior with replica symmetry breaking, it
manifestly has ``strong'' temperature chaos. We also show why chaos appears
only very slowly with system size.
