  This work continues the study of the thermal Hamiltonian, initially proposed
by J. M. Luttinger in 1964 as a model for the conduction of thermal currents in
solids. The previous work [DL] contains a complete study of the "free" model in
one spatial dimension along with a preliminary scattering result for
convolution-type perturbations. This work complements the results obtained in
[DL] by providing a detailed analysis of the perturbation theory for the
one-dimensional thermal Hamiltonian. In more detail the following result are
established: the regularity and decay properties for elements in the domain of
the unperturbed thermal Hamiltonian; the determination of a class of
self-adjoint and relatively compact perturbations of the thermal Hamiltonian;
the proof of the existence and completeness of wave operators for a subclass of
such potentials.
