They'll really need the heat at night too. You could try things like a hot water bottle in there but you'd have to keep getting up and changing it. Without creating a fire hazard, can you cordon off that area so it won't be quite so bright while you're trying to sleep? The lamps don't seem to keep the chicks up at night but they don't settle down and sleep all night either. Expect on and off peeping throughout the night.
