  The low-temperature thermal conductivity $\kappa$ of the spin-ice compound
Dy$_2$Ti$_2$O$_7$ shows pronounced hysteresis as a function of magnetic field.
Here, we investigate how these hysteresis effects depend on temperature, the
magnetic-field direction, the rate of magnetic-field change, and on the
direction of the heat current. In addition, the time-dependent relaxation of
the heat conductivity is investigated. These measurements yield information
about possible equilibrium states and reveal that in the low-field and
low-temperature region extremely slow relaxation processes occur.

Strongly Correlated Electrons