Abstract : While the existence of an island of stability beyond Z=110 is theoretically acquired, the location of this island ranges from Z=114 to Z=126 depending on models. In this work, the stability of super-heavy nuclei is probed through the study of their fission time. The chosen experimental method, the crystal blocking method, is sensitive to the presence of possible long time components in the fission time distribution which indicates a fission mechanism occurring after the formation of a compound nucleus. The blocking dips were therefore constituted for the various products of the reaction 238U+Ni (6.6 MeV/A)->120, the experimental set-up allowing us to clearly identify and select the reaction mechanisms. The comparison of the blocking dip constituted for quasi-elastic scattering events with the one obtained for the fission fragments of a Z=120, combined with the study of kinematical properties of these fission fragments, give evidences of the existence of very long fission times (> 10^-18s) only compatible with a fusion-fission mechanism implying a non vanishing fission barrier height for Z=120.
The second part outlines microscopic calculations of fission barrier heights, carried out in the framework of the finite temperature HFB theory. Because of the progressive vanishing of the pairing correlation with T, which happens differently at the ground state and at the top of the barrier, Bf first grows until T~0.8 MeV before dropping with T owing to shell-effects damping with temperature.