You only have to remember the link you just followed. Basically, make a boolean "followedThread" and initialize to false. Then, go to the root and follow this algorithm

    if (!followedThread && left != null) 
        set followedThread <- curNode.left.isThread
        set curNode <- curNode.left.node
    else
        set followedThread <- curNode.right.isThread
        set curNode <- curNode.right.node

Only node you really have to special case is the root node, and you can do that by making its right.node == null. Then you just do this while curNode != null.

That make sense? (Also... very possible that I made a mistake here...)