Quip: But when the patient's temp is high enough, everyone in the ER knows that you gotta go straight to the ice-water bath.

How many square miles of solar reflector could each Starship launch carry to a stable-ish region near the Earth-Sun L1 point?

Reflectors act as solar sails and hence need a fuel supply to stay put.

They need active guidance systems. Being solar sails - with a competent design, they can be trimmed (small portions of the sails moved with electric motors to adjust the forces from the sun) for station-keeping.

I'm not sure how you'd trim solar sails so that the sun doesn't push them to a more distant orbit. I don't think sailing against the solar wind is possible.