I have used boiling water with styrene and resin parts. In the case of my wood chip cars which were made from a flat cast styrene kit, they were very warped. I made a precisely fitting wooden block that held the shape and submerged it in the boiling water for a few seconds. It worked beautifully.
In the case of my resin parts, I had some long flat pieces that were rippled, like they had waves. I lashed then to pencils with dental floss and then dipped it in boiling water.
Both cases worked very well. If others know that FUD/FXD will soften in water then I say go for it. Just make sure it's well secured to that piece of wood that you mentioned.
Craig