  Quantum steering is a kind of quantum correlations stronger than entanglement
but weaker than Bell-nonlocality. In an optomechanical system pumped by
squeezed light and driven in the red sideband, we study-under thermal
effects-stationary Gaussian steering and its asymmetry of two mechanical modes.
In the resolved sideband regime using experimentally feasible parameters, we
show that Gaussian steering can be created by quantum fluctuations transfer
from the squeezed light to the two mechanical modes. Moreover, one-way steering
can be observed by controlling the squeezing degree or the environmental
temperature. A comparative study between Gaussian steering and Gaussian
R\'enyi-2 entanglement of the two considered modes shows on one hand that both
steering and entanglement suffer from a sudden death-like phenomenon with early
vanishing of steering in various circumstances. On the other hand, steering is
found stronger than entanglement, however, remains constantly upper bounded by
Gaussian R\'enyi-2 entanglement, and decays rapidly to zero under thermal
noise.
