  We investigate charm production in an equilibrated quark-gluon plasma
produced in heavy-ion collisions at RHIC and LHC. Effective quark and gluon
masses are introduced from thermal QCD calculations. Assuming a Bjorken-type
longitudinal expansion and including the influence of temperature dependent
masses on the expansion, we determine the total number of c\bar{c} pairs
produced in the quark-gluon plasma phase. We calculate the charm production
rate at leading order with massive gluons and quarks and compare our result to
charm production by massless partons. We consider two different scenarios for
the initial conditions, a parton gas with a rather long kinetic equilibration
time and a minijet gas with a short equilibration time. In a parton gas,
assuming m_c=1.2 GeV, we obtain a substantial enhancement over the thermal
charm rate from massless quarks and gluons, up to 4.9 secondary charm quark
pairs in Au+Au collisions at RHIC and 245 charm pairs in Pb+Pb collisions at
the LHC.
