The supply valve on the window fogs up inside - how do I fix this?

The fogging of the valve is condensation that forms when warm air from the room meets the cold incoming air flow. Usually it's a sign that the humidity in the space is too high or the valve is letting in too much cold air at once. Try lowering the humidity - ventilate more often but for shorter periods (5 - 10 minutes instead of leaving a gap open all day), make sure you're not air-drying laundry right in the room, and check that the kitchen and bathroom exhaust fans are working. If your valve has an adjustment, close it a bit - the cold air will come in more gently and won't create such a temperature contrast.