  We introduce a simple model to calculate the nuclear moment of inertia at
finite temperature. This moment of inertia describes the spin distribution of
nuclear levels in the framework of the spin-cutoff model. Our model is based on
a deformed single-particle Hamiltonian with pairing interaction and takes into
account fluctuations in the pairing gap. We derive a formula for the moment of
inertia at finite temperature that generalizes the Belyaev formula for zero
temperature. We show that a number-parity projection explains the strong
odd-even effects observed in shell model Monte Carlo studies of the nuclear
moment of inertia in the iron region.
