  We demonstrate that a periodically driven quantum system can adopt a
quasistationary state which is effectively much colder than a thermal reservoir
it is coupled to, in the sense that certain Floquet states of the
driven-dissipative system can carry much higher population than the ground
state of the corresponding undriven system in thermal equilibrium. This is made
possible by a rich Fourier spectrum of the system's Floquet transition matrix
elements, the components of which are addressed individually by a suitably
peaked reservoir density of states. The effect is expected to be important for
driven solid-state systems interacting with a phonon bath predominantly at
well-defined frequencies.
