I took Aidan's COMSOL model for the ITM from a couple years ago and updated it with some more details:
In the attached image, I have made one quadrant of the tubular cryo shield transparent just for clarity - the actual modelled tube is 3 cm thick, made of aluminum, has an emissivity of 0.95 on the inside and 0.03 on the outside (to simulate what we would get from polished aluminum or gold coating).
This files is in our GitLab: https://git.ligo.org/rana-adhikari/CryogenicLIGO/blob/master/FEA/ITM-ColdShield-CP.mph
*I am suspicious of just using a single emissivity number for the AR and HR coatings. Since we are concerned with wavelengths which are long w.r.t. the coating thickness, it may be that the HR and AR coatings have a complicated wavelength dependence in the 5-50 micron band.