I've built a box to help speed up the drying process for wood I had cut to make long bows. The staves were about 2 inches square and 6.5 feet long. Same principal as you barrel, however, I made mine out of plywood and lined it with some cheap insulation. I believe it had two light bulbs in it hooked up to a dimmer. I had a small meat thermometer sticking into the bow about half way between the two bulbs and used the dimmer to keep the temp around 110F. I had a small computer fan in one end and a adjustable air vent on the other end of the box. For green wood, the forced air really help drop the moisture content quickly. I had a moisture meter to check the progress on my staves, but the weighing trick works well. You might want to test a scrap peice of wood if using the fan because as metioned above, some woods do not take drying well and the fan may cause cracking. Typically wood left in the attic or garage will only reach a moisture content that is in equalibrium with the sorroundings, so if you live in Las Vegas versus New Orleans the same piece of wood keep in the garage will have a very large difference in moisture content. The heat box and fan can bring the moisture down to a level below that of your surroundings so I think this would help prior to stabilizing. You can probably check online but I think you would want the moisture content to be as low as possible without cracking prior to stabilizing. Good luck.
Mark