Building on [2643], I realized that the conductive cooling term proportional to  was also negligible. I added back in physical parameters for the 2 radiative terms (one from the cold plate, one from 295K) and used the emissivities of the test mass and inner shield as fit parameters:

I used Koji’s input to model radiative heating from 295K. I approximated the radius of the aperture (from which room temperature could be exposed) to be 3cm, and assumed radiative heat is emitted from this circle. 

The result of this fit can be seen in Attachment 1: [e_testmass, e_innershield] = [0.59736291, 0.20177643]. This would imply that Aquadag has an emissivity of about 0.6, and that the emissivity of rough aluminum is much higher than expected at 0.2.

I then used these parameters to model the cooldown, given: 1. both the test mass and inner shield surfaces are painted in Aquadag; 2. only the inner shield surface is painted in Aquadag. These models are shown in Attachment 2. 

Painting the inner shield in addition to the test mass would yield marginal improvement, as expected. However, painting the inner shield while removing Aquadag from the test mass would, according to this model, weaken the coupling further compared to the reverse case. This makes sense, since in Fe the effect of the inner shield’s emissivity is scaled by the ratio , which is quite small. Increasing the emissivity of the test mass therefore makes more of a difference in the coupling.