  The interactions of heavy quarks with the partonic environment at finite
temperature $T$ and finite quark chemical potential $\mu_q$ are investigated in
terms of transport coefficients within the Dynamical Quasi-Particle model
(DQPM) designed to reproduce the lattice-QCD results (including the partonic
equation of state) in thermodynamic equilibrium. These results are confronted
with those of nuclear many-body calculations close to the critical temperature
$T_c$. The hadronic and partonic spatial diffusion coefficients join smoothly
and show a pronounced minimum around $T_c$, at $\mu_q=0$ as well as at finite
$\mu_q$. Close and above $T_c$ its absolute value matches the lQCD calculations
for $\mu_q=0$. The smooth transition of the heavy quark transport coefficients
from the hadronic to the partonic medium corresponds to a cross over in line
with lattice calculations, and differs substantially from perturbative QCD
(pQCD) calculations which show a large discontinuity at $T_c$. This indicates
that in the vicinity of $T_c$ dynamically dressed massive partons and not
massless pQCD partons are the effective degrees-of-freedom in the quark-gluon
plasma.
