We analyze cooling of a nano-mechanical resonator coupled to a dissipative
solid state two level system focusing on the regime of high initial
temperatures. We derive an effective Fokker-Planck equation for the mechanical
mode which accounts for saturation and other non-linear effects and allows us
to study the cooling dynamics of the resonator mode for arbitrary occupation
numbers. We find a degrading of the cooling rates and eventually a breakdown of
cooling at very high initial temperatures and discuss the dependence of these
effects on various system parameters. Our results apply to most solid state
systems which have been proposed for cooling a mechanical resonator including
quantum dots, superconducting qubits and electronic spin qubits
