The height of the fencing isn't really that important. I put up a 6' tall fence of 2"x4" welded wire because I wanted to keep deer out as well as keeping my turkeys in. A 4' tall fence will most likely be sufficient. The most important thing about building a fence to keep turkeys in is do not put up a top rail. A top rail is extremely inviting to any turkey to hop up on and perch there. Unfortunately it seems like they get down on the wrong side of the fence far more often than not.
Thank you, R2elk. Our feedstore recommended chicken wire in a roll that we could unroll and staple to the trees. Do you have an opinion about that? I'd curve it around to lead Tommy back into our yard. My husband said he'll just go around. But if I use 150 feet of it - without fencing in our whole property I'm not sure of another solution.