  The thermal relaxation rate of open-charm ($D$) mesons in hot and dense
hadronic matter is calculated using empirical elastic scattering amplitudes.
$D$-meson interactions with thermal pions are approximated by $D^*$ resonances,
while scattering off other hadrons ($K$, $\eta$, $\rho$, $\omega$, $K^*$, $N$,
$\Delta$) is evaluated using vacuum scattering amplitudes as available in the
literature based on effective Lagrangians and constrained by realistic
spectroscopy. The thermal relaxation time of $D$-mesons in a hot $\pi$ gas is
found to be around 25-50\,fm/$c$ for temperatures $T$=150-180\,MeV, which
reduces to 10-25\,fm/$c$ in a hadron-resonance gas. The latter values, argued
to be conservative estimates, imply significant modifications of $D$-meson
spectra in heavy-ion collisions. Close to the critical temperature ($T_c$), the
spatial diffusion coefficient ($D_s$) is surprisingly similar to recent
calculations for charm quarks in the Quark-Gluon Plasma using non-perturbative
$T$-matrix interactions. This suggests a possibly continuous minimum structure
of $D_s$ around $T_c$.
