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.