  We present a study on how to realize the widely interested optomechanical
entanglement at high temperature. Unlike the majority of the previous
experimental and theoretical researches that consider the entanglement of a
mechanical resonator with a cavity field created by red-detuned continuous-wave
or blue-detuned pulsed driving field, we find that applying blue-detuned
continuous-wave pump field to cavity optomechanical systems can achieve
considerable degrees of quantum entanglement, which is generally challenging to
obtain at high temperature for the known physical systems. The competition
between the induced squeezing-type interaction and the existing decoherence
leads to stable entanglement in dynamically unstable regime. There is a much
more relaxed condition for the existence of entanglement, as compared with the
well-known criterion for neglecting the thermal decoherence on optomechanically
coupled systems. A simple relation about a boundary in the parameter space,
across which the entanglement can exist or not, is found with an analytical
expression for the degree of the achieved entanglement at any temperature,
which is derived for the systems of highly resolved sideband. The studied
scenario with blue-detuned continuous-wave driving field can greatly simplify
the generation of the widely interested optomechanical entanglement of
macroscopic quantum states. Our study also provides the answers to two
fundamentally meaningful open problems: (1) what is the condition for a system
to avoid its loss of quantum entanglement under thermal decoherence? (2) is it
possible to preserve the entanglement in a thermal environment by increasing
the interaction that entangles the subsystems?
