We calculate excitation functions for open charm mesons in Au + Au reactions from AGS to RHIC energies within the HSD transport approach which is based on string, quark, diquark (q, (q) over bar, qq, (q) over bar(q) over bar) and hadronic degrees of freedom. The open charm cross sections from pN and piN reactions are fitted to results from PYTHIA and scaled in magnitude to the available experimental data. From our dynamical calculations we find an approximate m(T)-scaling for pions, kaons, D mesons and J/psi - when discarding final-state elastic scattering of kaons and phi mesons with pions - in central collisions of Au + Au at 160 A GeV (with an apparent slope of 176 MeV) without employing the assumption of a Quark-Gluon Plasma (QGP). We demonstrate that this result is essentially due to a relative m(T)-scaling in pp collisions at roots approximate to 17.3 GeV. At lower bombarding energies of 25 A GeV a suppression of D mesons by a factor of similar to 10 relative to a global m(T)-scaling with slope 143 MeV is expected. However, when incorporating attractive D-meson self-energies as suggested by QCD sum rules, an approximate m(T)-scaling is regained even at 25 A GeV. The effects of D-meson rescattering and charmonium absorption are discussed, furthermore, with respect to rapidity and transverse mass distributions in central collisions of Au + Au at 25, 160 A GeV and 21.3 A TeV. (C) 2001 Elsevier Science B.V. All rights reserved.