  We investigate how dynamic correlations of hard-core bosonic excitation at
finite temperature are affected by additional interactions besides the
hard-core repulsion which prevents them from occupying the same site. We focus
especially on dimerized spin systems, where these additional interactions
between the elementary excitations, triplons, lead to the formation of bound
states, relevant for the correct description of scattering processes. In order
to include these effects quantitatively we extend the previously developed
Br\"uckner approach to include also nearest-neighbor (NN) and next-nearest
neighbor (NNN) interactions correctly in a low-temperature expansion. This
leads to the extension of the scalar Bethe-Salpeter equation to a matrix-valued
equation. Exemplarily, we consider the Heisenberg spin ladder to illustrate the
significance of the additional interactions on the spectral functions at finite
temperature which are proportional to inelastic neutron scattering rates.
