Heating a surface above the dew point helps prevent condensation.
Radiant heat is better at this than warming the air, which transfers its heat poorly to objects.
Of course, closing the curtains means that most if any radiant heat will be absorbed before it reaches the inner pane of the windows
http://en.wikipedia.org/wiki/Dew_point
Ventilating a space to reduce water vapour in the air below saturation helps prevent condensation.
Local ventilation near a source of water vapour is more efficient than general space ventilation - eg a cooker hood or extract vent above a shower, both vented to a heat exchanger or direct to external air.
Human activity (sweating, cooking, washing, breathing) in sealed poorly ventilated spaces tends to increase condensation.
Athletic levels of exercise within an apartment followed by showering and a steamed, boiled or friend meal would be an example.
If you don't properly ventilate a dwelling, moisture can build up over time in the surfaces of fabrics and walls leading to the growth of damp and bacteria.
This is more likely to occur during extended periods of colder, wetter weather
ONQ.
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Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matter at hand.