I make wooden bows for archery and in doing so have bent wood hundreds of times to manipulate its shape or take out warp or twist. Wade is right, it's heat that makes wood limber, allows it to be moved, and then stay there when it cools. Various wood types have differing amounts of spring back, so overcorrect slightly. 5 - 10%. Merely soaking it adds a lot of moisture and it will need dried again. It may warp even worse as it does.
If it was dry wood, and a relatively small area that needed corrected, say a foot or two long, I'd use a heat gun. For a longer or thicker area, I'd use steam. I made a cheap and easy steam tube with 4" galvanized pipe, with a T in the middle. The T fits nicely in one of those ceramic coated camp coffee pots full of water, which sits on a hot plate. Steam for approximately 1 hour per inch of thickness.
If it fits, you can also steam the area over a big pot, or roasting pan of boiling water on the stove. Just build a tent over it with aluminum foil, retaining the steam while allowing it to slowly vent along the wood on either side. Steam is the vehicle that carries the heat along and into the wood.
If you soaked it and it absorbed a lot of moisture, a heat gun would try to dry it very quickly and it could cause drying checks. Steaming would be a safer bet.