A limiting factor here is the amount of wood you have. After picking pieces for density, and then visually selecting ones that didn't have high porosity and parallel grain, I didn't have the luxury of throwing out quarter grain because I barely had enough balsa to build a structure with. OM structure can be an expensive problem. I've heard of teams spending hundreds of dollars a year on balsa. If you go to any OM competition you'll see people using hair driers, homemade ovens, and dessicants on their structures before weigh-in.
Balsa wood is very porous and as a result picks up moisture from the air quite readily.
To drive off the water, teams use the methods mentioned above. The method I use is the hair drier. I try to find an electrical outlet near weigh in, and take a balance with me. In past years I've used aluminum foil to make a shell around the structure and direct the airflow. In Division IV I tried a new approach, using a turkey oven basting bag.