  Mesons with heavy flavor content are an exceptional probe of the hot QCD
medium produced in heavy-ion collisions. In the past few years, significant
progress has been made toward describing the modification of the properties of
heavy mesons in the hadronic phase at finite temperature. Ground-state and
excited-state thermal spectral properties can be computed within a
self-consistent many-body approach that employs appropriate hadron-hadron
effective interactions, providing a unique opportunity to confront hadronic
Effective Field Theory predictions with recent and forthcoming lattice QCD
simulations and experimental data. In this article, we revisit the application
of the imaginary-time formalism to extend the calculation of unitarized
scattering amplitudes from the vacuum to finite temperature. These methods
allow us to obtain the ground-state thermal spectral functions. The thermal
properties of the excited states that are dynamically generated within the
molecular picture are also directly accessible. We present here the results of
this approach for the open-charm and open-bottom sectors. We also analyze how
the heavy-flavor transport properties, which are strongly correlated to
experimental observables in heavy-ion collisions, are modified in hot matter.
In particular, transport coefficients can be computed using an off-shell
kinetic theory that is fully consistent with the effective theory describing
the scattering processes. The results of this procedure for both charm and
bottom transport coefficients are briefly discussed.
