  The dynamical Casimir effect is the physical phenomenon where the mechanical
energy of a movable wall of a cavity confining a quantum field can be converted
into quanta of the field itself. This effect has been recognized as one of the
most astonishing predictions of quantum field theory. At the quantum scale, the
energy conversion can also occur incoherently, namely without an physical
motion of the wall. We employ quantum thermodynamics to show that this
phenomenon can be employed as a tool to cool down the wall when there is a
non-vanishing temperature gradient between the wall and the cavity. At the same
time, the process of heat-transfer enables to share the coherence from one
cavity mode, driven by a laser, to the wall, thereby forcing its coherent
oscillation. Finally, we show how to employ one laser drive to cool the entire
system including the case when it is composed of other subsystems.
