Just put a shade or blinds in the window and keep it closed.

I should have mentioned that covering the window is not an option

Since you can't or won't cover the widow, you could install IKEA wire curtain rods, and curtain panels to cover the hanging space. Easy to open and close.

Have the window coated with UV film.

I second the film. HD or Lowes sells a cheap version, don't spend a lot for a closet.