Sweaty walls happen when there is not sufficient insulation. Like condensation on a pitcher of ice water, when the walls are cold and the air is warm, condensation happens. The problem is that condensation on walls can cause mold growth. Woodbridge Environmental, a contractor near Elizabeth, NJ, suggests venting the house to remove moisture. Running a dehumidifier can help. He also suggests venting the house's heater. Another suggestion is to insulate the wall cavities better.