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Quantum steering is a kind of quantum correlations stronger than entanglementbut weaker than Bell-nonlocality. In an optomechanical system pumped bysqueezed light and driven in the red sideband, we study-under thermaleffects-stationary Gaussian steering and its asymmetry of two mechanical modes.In the resolved sideband regime using experimentally feasible parameters, weshow that Gaussian steering can be created by quantum fluctuations transferfrom the squeezed light to the two mechanical modes. Moreover, one-way steeringcan be observed by controlling the squeezing degree or the environmentaltemperature. A comparative study between Gaussian steering and GaussianR\'enyi-2 entanglement of the two considered modes shows on one hand that bothsteering and entanglement suffer from a sudden death-like phenomenon with earlyvanishing of steering in various circumstances. On the other hand, steering isfound stronger than entanglement, however, remains constantly upper bounded byGaussian R\'enyi-2 entanglement, and decays rapidly to zero under thermalnoise.

Controlling Stationary One-Way Steering via Thermal Effects in Optomechanics