1) Is this a wall-to-wall carpet? If so, have you verified that there isn't water getting in under an edge of a wall? Are you sure there's no leak of any kind in the roof, walls, etc.?
2) What kind of heating/cooling is in the room? Is it the same as the rest of the house? Does the room have any ventilation?
3) Are other items in the room (such as furniture) equally as damp as the carpet?
4) Are there any exposed pipes or vents in the room that might sweat?
5) Have you considered a dehumidifier?

Thanks for your reply. it is wall to wall carpet, but the edges are actually dry and the middle of the floor has the most dampness, I really don't believe that there are and roof/wall leaks ( I have looked). The whole house is heated with forced hot air, the original heat was electric baseboard this however is not working in this room (lower on the to-do list!) There is significant ventilation with several windows covering 2 sides of the addition. The furniture isn't damp except for the wicking that occurs up the legs where it contacts the carpet. There is no plumbing or vents in this part of the house. Due to the amount of exposure to the outside and no door seperating this room from the rest of the house, I don't think a dehumidifier would be effective. I could air-condition the house but we try not to run the AC to save money.