  We study a concrete model of a confined particle in form of a Schr\"odinger
operator with a compactly supported smooth potential coupled to a bosonic field
at positive temperature. We show, that the model exhibits thermal ionization
for any positive temperature, provided the coupling is sufficiently small.
Mathematically, one has to rule out that zero is an eigenvalue of the
self-adjoint generator of time evolution - the Liouvillian. This will be done
by using positive commutator methods with dilations in the space of scattering
functions. Our proof relies on a spatial cutoff in the coupling but does
otherwise not require any unnatural restrictions.
