  We report on microwave optomechanics measurements performed on a nuclear
adiabatic demagnetization cryostat, whose temperature is determined by accurate
thermometry from below 500$~\mu$K to about 1$~$Kelvin. We describe a method for
accessing the on-chip temperature, building on the blue-detuned parametric
instability and a standard microwave setup. The capabilities and sensitivity of
both the experimental arrangement and the developed technique are demonstrated
with a very weakly coupled silicon-nitride doubly-clamped beam mode of about
4$~$MHz and a niobium on-chip cavity resonating around 6$~$GHz. We report on an
unstable intrinsic driving force in the coupled microwave-mechanical system
acting on the mechanics that appears below typically 100$~$mK. The origin of
this phenomenon remains unknown, and deserves theoretical input. It prevents us
from performing reliable experiments below typically 10-30$~$mK; however no
evidence of thermal decoupling is observed, and we propose that the same
features should be present in all devices sharing the microwave technology, at
different levels of strengths. We further demonstrate empirically how most of
the unstable feature can be annihilated, and speculate how the mechanism could
be linked to atomic-scale two level systems. The described
microwave/microkelvin facility is part of the EMP platform, and shall be used
for further experiments within and below the millikelvin range.
