Soak towels in warm water and lay them on a driveway, or patio in direct sunlight. Spread enough towels to hold all of your warped barn wood. Allow the towels to warm up for one hour so that they are warm to the touch.
Turn the barn wood so that the bowed side is up and the cupped, or concave, side is down. Position the boards on the towels with enough space at the ends for the boards to lay full length, when straightened.
Lay sheets of plywood on top of your barn wood, to aid in pressing it flat. Roll out black plastic on top of the plywood and cut it to fit. Position cinder blocks on all four corners and in the center of each plywood sheet.
Allow the wood to sit in the sun all day. Remove the blocks, plastic and plywood. Check the barn wood for results. Remove pieces that are straight enough to be used and set them aside.
Apply hot water with a sponge to the cupped face of the remaining boards, one at a time. Place a damp towel on top and run a hot iron over it to force the moisture into the grain as steam. Do this for each board.
Turn the boards over and run a dry iron over the convex side to apply dry heat, shrinking the grain. Continue with this treatment until the wood begins to straighten.
Place a cinder block on top of each board remaining, so that it presses the curve down, flat to the driveway or patio. Leave this weight in place overnight. Boards that still do not straighten are probably a lost cause.