The internal energy and chemical potential of a noninteracting Fermi gas has been evaluated in three ways: numerically (applicable to arbitrary temperatures), through an asymptotic power series expansion (suitable for low temperatures), and by means of standard Padé approximants (appropriate for low and moderate temperatures). The main conclusion of this work is that the Padé approximant, which is constructed from the asymptotic series employing only minimal labor, is far superior to the truncated series expansion.