  Dynamic correlations of quantum magnets provide valuable information.
However, especially at finite temperature, many observations, e.g., by
inelastic neutron scattering experiments, are not yet quantitatively
understood. Generically, the elementary excitations of gapped quantum magnets
are hardcore bosons because no two of them can occupy the same site. The
previously introduced diagrammatic Br\"uckner approach dealt with hardcore
bosons of a single flavor at finite temperature. Here, this approach is
extended to hardcore bosons of several kinds (flavors). The approach based on
ladder diagrams is gauged with so far unknown rigorous results for the thermal
occupation function of multiflavored hardcore bosons in one dimension with
nearest-neighbor hopping. For low temperatures, it works very well.
Furthermore, we study to which extent the approach is a conserving
approximation. Empirical evidence shows that this is true only in the
single-flavor case.
