Large-scale macroscopic-microscopic calculations taking into account thermal effects are performed in the mass A similar to 130 nuclei to search for hyper-deformation (HD). An emphasis is set on the role of the Jacobi shape transition for the population of hyper-deformed states. The hyper-deformed configurations are predicted to exist at the very high spins only, in contrast to the super-deformed ones. Moments of inertia are calculated and compared with experiment, showing good agreement