  We consider a $W^*$-dynamical system $(\Mg,\taug)$, which models finitely
many particles coupled to an infinitely extended heat bath. The energy of the
particles can be described by an unbounded operator, which has infinitely many
energy levels. We show existence of the dynamics $\taug$ and existence of a
$(\beta,\taug)$ -KMS state under very explicit conditions on the strength of
the interaction and on the inverse temperature $\beta$.
