I agree that you need to fix the problem first. However, if that's not going to happen, here's an idea: affix a wall-mounted radiator / towel-rail / heater to that section of the wall and run it 24/7. It will dry out the damp plasterboard.
Sure, it's going to steadily rotting-away behind but at least it won't show in the room.
Be aware though that that water has to go somewhere as it dries and so also, a dehumidifier needed.
Edit: be mindful of the close-proximity of the curtain. It could overheat any heater placed nearby.