  The property of ``{\it return to equilibrium}'' is established for a class of
quantum-mechanical models describing interactions of a (toy) atom with
black-body radiation, or of a spin with a heat bath of scalar bosons, under the
assumption that the interaction strength is {\it sufficiently weak}. For models
describing the first class of systems, our upper bound on the interaction
strength is {\it independent} of the temperature $T$, (with $0<T\leq
T_0<\infty$), while, for the spin-boson model, it tends to zero
logarithmically, as $T\to 0$. Our result holds for interaction form factors
with physically realistic infrared behaviour.
  Three key ingredients of our analysis are: a suitable concrete form of the
Araki-Woods representation of the radiation field, Mourre's positive commutator
method combined with a recent virial theorem, and a norm bound on the
difference between the equilibrium states of the interacting and the
non-interacting system (which, for the system of an atom coupled to black-body
radiation, is valid for {\it all} temperatures $T\geq 0$, assuming only that
the interaction strength is sufficiently weak).
