  We find a dynamic effect in the non-equilibrium dynamics of a spin glass that
closely parallels equilibrium temperature chaos. This effect, that we name
dynamic temperature chaos, is spatially heterogeneous to a large degree. The
key controlling quantity is the time-growing spin-glass coherence length. Our
detailed characterization of dynamic temperature chaos paves the way for the
analysis of recent and forthcoming experiments. This work has been made
possible thanks to the most massive simulation to date of non-equilibrium
dynamics, carried out on the Janus~II custom-built supercomputer.
