[en] An extension of the statistical model for the study of very excited nuclei is presented. The temperature and angular momentum dependences of the fission barriers are obtained in a liquid drop picture. It provides us with the relevant potential landscapes for some collective variables which evolve during the decay according to a generalized transport equation. The light particle evaporation during the fast fission process and the fission after compound nucleus formation is calculated and compared with some available experimental results, e.g. for ⁴⁰Ar + ²³⁸U at 27 MeV/u. The competing process of particle emission (cooling) during the thermal equilibrium prevents a complete transfer of excitation energy along the whole evolution of the system. Such nuclei should be called warm instead of hot