  We propose a scheme to cool down a mechanical resonator to its quantum
ground-state, which is interacting with a working fluid via an
optomechanical-like coupling. As opposed to standard laser cooling schemes
where coherence renders the motion of a resonator to its ground-state, we
consider an incoherent thermal source to achieve the same aim. We show that
simultaneous cooling of two degenerate or near-degenerate mechanical resonators
is possible, which is otherwise a challenging goal to achieve. The
generalization of this method to the simultaneous cooling of multiple
resonators is straightforward. Spectral filtering of the coupling between the
cooling agent and the baths is a key to realize cooling in our scheme. The
underlying physical mechanism of cooling is explained by investigating a direct
connection between the laser sideband cooling and cooling by heating in a
standard optomechanical setting. Our advantageous scheme of cooling enabled by
quantum reservoir engineering can be realized in various setups, employing
parametric coupling of a cooling agent with the target systems. We also discuss
using non-thermal baths to simulate ultra-high temperature thermal baths for
cooling.
