  We demonstrate an accurate method to control the motion of a micromechanical
oscillator in contact with a thermal bath. The experiment is carried out on the
cantilever tip of an Atomic Force Microscope (AFM). Applying an appropriate
time dependent external force, we decrease the time necessary to reach
equilibrium by two orders of magnitude compared to the intrinsic equilibration
time. Finally, we analyze the energetic cost of such a fast equilibration, by
measuring with kBT accuracy the energy exchanges along the process.
