  We study the laser cooling of a mechanical oscillator through the coupling
with a dissipative three-level system. Under a background temperature beyond
the Lamb-Dicke regime, we extend the standard cooling analysis by separately
studying the classical motion and the quantum dynamics of the oscillator. In
Ladder-system cooling, the cooling rate degrades by orders of magnitude at
large classical motion. This phenomenon causes a critical transition of the
final temperature at a hot background. In stark contrast,
electromagnetic-induced-transparency (EIT) cooling with a $\Lambda$-system
produces significant negative cooling rate at high motional excitation. At
steady state, the oscillator could exhibit both cooling and lasing behaviours.
We argue that a successful EIT cooling requires either a poor quality
oscillator to suppress the lasing effect, or terminating the cooling process at
a transient stage.
