  A consistent framework for treating the energy dependence of fission-fragment
neutron multiplicities is presented. The shape evolution of the compound
nucleus towards scission is treated in the strong damping limit using the
Metropolis walk method. The available excitation energy at scission is then
divided statistically between the two fragments using microscopic level
densities. Deformation energies, which contribute to the excitation energy when
the fragments relax to their ground-state shapes, are also computed. From the
total fragment excitation energies, the number of emitted neutrons is obtained
and illustrated for neutron-induced fission of $^{235}\textrm{U}$.
