  Procedures for projecting angular momentum in a model describing a hot
nucleus that takes into account large-amplitude quadrupole fluctuations are
discussed. Particular attention is paid to the effect angular-momentum
projection has on the observables associated with the $\gamma$-decay of the
giant-dipole resonance (GDR). We also elaborate on which of the different
projection methods provides the best overall description of the GDR, including
angular distributions. The main consequence of angular-momentum projection is
the appearance of an effective volume element in the integrals associated with
the thermal average of the physical observables. This effective volume element
is controlled by the value of the moments of inertia of the system. In the
limit of rigid-body moments of inertia, the effective volume element is found
to differ only slightly from the volume element associated with the
normalization of the five-dimensional quadrupole oscillator wavefunction in the
$\beta$, $\gamma$, and $\Omega$ space, namely $D[\alpha]=\beta^4d\beta
sin(3\gamma)d\gamma d\Omega$. In the limit of irrotational flow moments of
inertia, the leading behavior in the $\beta$ degree of freedom is
$D[\alpha]\propto \beta d\beta$.
