Numerical simulations provide an increasingly detailed picture of the build-up of the stellar mass of galaxies, but they remain schematic in their description of the dissipative processes which regulate star formation. The mechanical energy released by mergers, gas accretion, the formation of bound systems and feedback must be dissipated for star formation to occur and proceed. Spectroscopy of warm H2 observations with the Spitzer Space Telescope and the SINFONI spectro-imager at ESO have unraveled an unexpected facet of the energetics of galaxy and star formation. They show that the dissipation processes involve the formation and dynamical heating of molecular gas. I present the physical understanding of the energetics of the multi-phase, turbulent interstellar medium, which arises from the observations and data modeling.