  Soft-clamped silicon nitride membrane resonators reach coherence times tau in
excess of 100 ms at milliKelvin bath temperatures. However, harnessing strong
optomechanical coupling in dry dilution refrigerators remains challenging due
to vibration issues and heating by optical absorption. Here, we propose to
address these issues with an actuator-free optical cavity and mechanical
resonator design, in which the cavity is mounted on a simple
vibration-isolation platform. We observe dynamical backaction when the cavity
is driven with a free-space optical beam stabilized close to the red sideband
using a two-beam locking scheme. Finally, we characterize the effect of
absorption heating on the coherence time, and find a scaling with the
intracavity power P as tau proportional to P to the power of -(0.34+/-0.04).
