Building on [32], I added a copper cold finger to conductively cool the inner shield, instead of holding the inner shield fixed at 77K. The cold finger draws cooling power from a cyro cooler or "cold bath" held at 60K, for simplicity. I added an outer shield and set its temperature to 100K. The outer shield supplies some radiative heating to the inner shield, but blocks out 295K heating, which is what we want. The expanded diagram can be seen in Attachment 1. 

I wanted to find the optimal choice of inner shield area (A_IS) to maximize the radiative cooling to the test mass. I chose 5 values for A_IS (from A_TM to A_OS) and plotted the test mass cooldown for each in Attachment 2. The radiative coupling between the inner shield and test mass is maximized when the ratio of the areas, A_TM/A_IS, is minimized. Therefore, the larger A_IS, the colder the test mass can be cooled. Even though choosing A_IS close to A_OS increases the coupling between the 2 shields, the resulting heating from the outer shield is negligible compared to the enhancement in cooling.

I chose A_IS = 0.22 m² to model the inner shield and test mass cooldown in Attachment 3. The test mass reaches 123 K at ~ 125 hours, or a little over 5 days. I have pushed the updated script which can be found under mariner40/CryoEngineering/MarinerCooldownEstimation.ipynb.