  In perturbative thermal calculations, introducing nonzero quark masses causes
considerable complications. In this article we describe an approximation scheme
valid for sufficiently light masses which significantly simplifies the relevant
calculations with only a small loss in accuracy. We apply the scheme to Quantum
Chromodynamics, with two massless and one massive flavor, obtaining analytic
results which are in excellent agreement with numerical non-approximated
results. Our results are accurate to $O(g^5)$ in the strong coupling parameter
$g$, as long as either the chemical potential $\mu$ of the quark species with
nonzero mass $m$ satisfies $m = O(g \mu)$ or if the temperature $T$ satisfies
$m = O(g T)$. We find that these conditions are always satisfied for the three
lightest quarks for the values of $\mu$, $T$ where Quantum Chromodynamics is
perturbatively convergent.
