  Accounting for viscous damping within Fokker-Planck equations led to various
improvements in the understanding and analysis of nuclear fission of heavy
nuclei. Analytical expressions for the fission time are typically provided by
Kramers' theory, which improves on the Bohr-Wheeler estimate by including the
time-scale related to many-particle dissipative processes along the deformation
coordinate. However, Kramers' formula breaks down for sufficiently high
excitation energies where Kramers' assumption of a large barrier no longer
holds. In the regime $T>1$ MeV, Kramers' theory should be replaced by a new
theory based on the Ornstein-Uhlenbeck first-passage time method that is
proposed here. The theory is applied to fission time data from fusion-fission
experiments on $^{16}$O+$^{208}$Pb $\rightarrow$ $^{224}$Th. The proposed model
provides an internally consistent one-parameter fitting of fission data with a
constant nuclear friction as the fitting parameter, whereas Kramers' fitting
requires a value of friction which falls out of the allowed range. The theory
provides also an analytical formula that in future work can be easily
implemented in numerical codes such as CASCADE or JOANNE4.
