As the answer to this thread states, cooling superconductors in spacecraft is necessary because of waste heat from secondary systems and thermal radiation of the sun. The application in which superconductors are the most interesting to me is magnetically shielding spaceships from solar wind and galactic cosmis rays to reduce the radiation risks for manned spaceflight.
What I'm thinking about is getting rid of anything superfluous, making the system as simple as possible and just shooting it away from the ship with a conductive tether connected to the superconductive coil, which is itself connected to a large and thin reflective film that blocks heat from the sun. After positioning the solar shade, the coil should slowly radiate away energy and eventually become superconductive (at 10 Kelvin for conventional niobium-titanium alloy), right? You could then gradually add current to the coil until the magnetic field is strong enough to block harmful radiation.
Problems I see with this approach:
1) Orienting the solar shade
You can never let the coil heat beyond its critical temperature, so the solar shade has to stay in front of the coil at all times. This probably requires thrusters and a computer, which makes the solar shade a kind of mini satellite in itself.
2) Tethers, secondary systems and waste heat
The electrical energy comes from the conductive tether which is not a superconductor itself, so there'll be waste heat. Deflecting charged particles will also take energy, you constantly have to add new current to the coil. On top of that you probably also need a computer and something to monitor and regulate the coil, producing even more waste heat.
3) Magnetic field strength
The farther the magnetic shield is from the spacecraft the smaller is the amount of protection you'll get. If you get too close to the ship, thermal radiation from it might heat up your superconductor and the magnetic field will affect metal inside of it. Does the required distance from the craft give you enough protection to make this worthwhile?
4) Shutting the coil off
You can let it heat beyond the critical temperature, but the superconducting material will quench and release a lot of heat, which might damage it.
All in all, is this actually a feasible idea compared to just using active cooling?