  We propose a generation of a low-noise state of optomechanical oscillator by
a temperature dependent force. We analyze the situation in which a quantum
optomechanical oscillator (denoted as the membrane) is driven by an external
force (produced by the piston). Both systems are embedded in a common heat bath
at certain temperature $T$. The driving force the piston exerts on the membrane
is bath temperature dependent. Initially, for $T=T_0$, the piston is linearly
coupled to the membrane. The bath temperature is then reversibly changed to
$T\neq T_0$. The change of temperature shifts the membrane, but simultaneously
also increases its fluctuations. The resulting equilibrium state of the
membrane is analyzed from the point of view of mechanical, as well as of
thermodynamic characteristics. We compare these characteristics of membrane and
derive their intimate connection. Next, we cool down the thermal noise of the
membrane, bringing it out of equilibrium, still being in the contact with heat
bath. This cooling retains the effective canonical Gibbs state with the
effective temperature $T^\star$. In such case we study the analogs of the
equilibrium quantities for low-noise mechanical states of the membrane.
