We report on direct measurements of the energy dissipated in the spin-up of the superfluid component of 3He-B. A vortex-free sample is prepared in a cylindrical container, where the normal component rotates at constant angular velocity. At a temperature of 0.20Tc, seed vortices are injected into the system using the shear-flow instability at the interface between 3He-B and 3He-A. These vortices interact and create a turbulent burst, which sets a propagating vortex front into motion. In the following process, the free energy stored in the initial vortex-free state is dissipated leading to the emission of thermal excitations, which we observe with a bolometric measurement. We find that the turbulent front contains less than the equilibrium number of vortices and that the superfluid behind the front is partially decoupled from the reference frame of the container. The final equilibrium state is approached in the form of a slow laminar spin-up as demonstrated by the slowly decaying tail of the thermal signal.