Yes, a curtain.
You can buy a "portiere rod" which looks like a brass or chrome curtain rod, but is designed so it swings open when you open the door and automatically lifts so it does not drag on the carpet. If it is in a kitchen, get a curtain in some easily-washable material. If it was some other room I'd recommend a heavy material fitted with curtain lining for better heat retention.
You can also get a plastic film that gives a temporary double glazing, it is stuck to the window frame to give an air gap. The panel at the bottom of the door could have a ply panel over, with insulation in the gap.
Also get a blind or curtain for that window.