For the Thermal Shields, I added some new coldheads, added radiation to the copper bar assuming it sees the bath everywhere, and added some code to evalute time to heat with some heaters. This last bit of code is super wierd and non-deterministic, so don't trust the graphs if they don't look physical.
I also wrote some brief code calculating what kind of thermal gradients the beamsplitter can support given some laser power is absorbed by the optic. A 12.5 K/W accross a 10 mm long, 2 mm side length square spoke. Assuming 0.1 W is absorbed, this is 1.25 K.
One consideration: will one part of the optic heat up more that another due to radiation from an inner shield at 242 K? I believe the answer is no given a uniform optic thickness, since both power abosrbed and thermal mass are proportional to area. This ignores how the beam splitter holder reduces how much certain parts of the beamsplitter see the inner shield. Because the total power on the optic is 0.2 W, this approximation doesn't need to be examined further and we should only worry about the laser power's effect on introducing gradients.