  Lattice calculations of the QCD trace anomaly at temperatures $T<160$ MeV
have been shown to match hadron resonance gas model calculations, which include
an exponentially rising hadron mass spectrum. In this paper we perform a more
detailed comparison of the model calculations to lattice data that confirms the
need for an exponentially increasing density of hadronic states. Also, we find
that the lattice data is compatible with a hadron density of states that goes
as $\rho(m) \sim m^{-a}\exp(m/T_H) $ at large $m$ with $a> 5/2$ (where $T_H
\sim 167$ MeV). With this specific subleading contribution to the density of
states, heavy resonances are most likely undergo 2-body decay (instead of
multi-particle decay), which facilitates their inclusion into hadron transport
codes. Moreover, estimates for the shear viscosity and the shear relaxation
time coefficient of the hadron resonance model computed within the excluded
volume approximation suggest that these transport coefficients are sensitive to
the parameters that define the hadron mass spectrum.
