You should still air it. Your body heat will, indeed, help evaporate some moisture but will generate more over the night.
A human body generates the same heat as a 100-watt light bulb but it's also creating humidity. It's so bad that during WWII when the Germans created massive shelters for thousands of people, the humidity generated by the bodies was so bad that it could rain inside and they had to improve the ventilation system by a lot.
Studies from the Canadian Military showed that the weight of a sleeping bag can increase by 30% because of human moisture, and this....in the Arctic! Also, if you stuff it immediately, you'll stuff it with moisture. That's bad! So always air dry your sleeping bag as much as possible.
Also, always use a liner to prevent your sleeping bag from becoming dirty inside. If it does, it'll clog it and there'll be more moisture inside. In winter, you can even use a moisture barrier. Oh joy of the down sleeping bags! :)