I had problems with fogging a few times when the AW1 was fairly new. It happened a couple of days after having used it in water, but I am not sure that had anything to do with it, going outside during a cool evening certainly had something to do with it. I have not seen it lately. The idea to keep it in a very dry place before closing it up should be good. Heating itself will not help as water vapor pressure (an thereby air humidity content) might stay the same or even increase, unless it helps to evaporate water in the liquid phase. I considered taking the battery out and storing the AW1 with a small packet of fresh regenerated silica gel in the battery chamber but never got around to it. There could be a problem with dust/particles if the packet is not well enough sealed. Also the lens interior is pretty isolated from the body's interior, so I am not sure it would help the lens. Storing the lens without rear cap in a sealed container with a good amount of fresh dessicant should help.
Another point is if has been it in water and then there is need to change battery or card, I try to let the camera dry before opening. Be very careful to get rid of all humidity around the seals before closing it up again. The same applies to the o-ring groove at the mount. Best to completely take the o-ring out and then clean the grove and the o-ring, relubricate, before assembling again. It sounds like you had not used it in water recently?
The Nikon recommended filter is very expensive for what it is; you might consider saving those funds for the Oympus wideangle converter lens, which would serve the same function and be better with respect to fogging underwater, although most effective with the 10mm lens.
If air is close to saturated with water vapor (for instance in a coastal climate) just a 7°C drop in temperature could theoretically be enough to cause condensation (well known among those using underwater housings). However the volume inside the AW1 is very small to hold much water vapor. One could speculate that some humidity is retained in circuit boards (perhaps even from the production stage) that warm up releasing the humidity.
In less sealed cameras, humidity will more easily escape and the interior equilibrate with the environment.