I hope you didn't pay any money to the company that did this, or if you did you should be demanding they come back out to your house and spend however long it takes to get most of the dampness out of your carpet. Carpet should be virtually dry after about 4 hours if done correctly.
If they won't come back out, you have a few options. Call another company and have them come out and reclean the carpet and charge the original company with the bill. If that doesn't work, go to Home Depot or Kroger (I think they still rent the machines) and rent of the carpet cleaning machines they have. Use a cleaner recommended by the machine maker (or just buy some of the Hoover chemical). The water in the carpet cleaner works best when hot, so you may want to put some water on the stove and heat it up to almost boiling temperature. Once you clean the room (and do this room-by-room), go back over it several times with just the vacuum running on the unit and pull as much water of the carpet as you can (this may take you the better part of the day with one of these machines). Once you have done this, then use your fans. Depending upon the outside humidity, you may want to open some windows (if the humidity is low). If you have space heaters, use them around the room. Keeping your AC on is a good idea to reduce humidity in the house, but keep in mind that the warmer the air in your house is, the more water vapor it will hold, so you may be shooting yourself in the foot by keeping it cold.