No, temperature does not decrease significantly when objects are in the shadows, unless hey stay there for a long time. Even when they don’t get energy from solar radiation, they still dissipate it by radiative transfer, which is very inefficient. So they cool down slowly.

I assume the idea is that they'll be in a solar orbit, so there will be a perpetually sun facing side and a perpetually shaded side. The exact physics behind radiating the heat out in this setup are unclear to me, but it seems difficult to imagine that it would pose significant, let alone insurmountable, difficulties.