I use time dependent option to simulate temperature change inside the mirror. The power input is DC + fluctuation.

Assuming RIN = 10^-4 @ 10 Hz, no coatings layer.

The plot below shows the absolute value of temperature fluctuation |(T - <T>)| on y-axis, and depth from the surface on x-axis.

Different lines (data 1 to 11) are different times in the substrate, from 20.0 to 20.1 sec with 0.01 time step.

It seems that the thermal length is quite large ~0.26 mm compared to what we got from half infinite model (~5 um).

dT from 1-D model is ~0.32 uK, while the result from COMSOL is ~1.8 uK.

If we use dT = 1.8 uK the frequency noise at 10 Hz will be (a factor of 6 larger) ~0.009 Hz/ rtHz. Still too low to see.