It sounds like the white smoke is just the burn off of any oil or coolant that may have gotten into the system. Is the smoking getting less?
Also i would probably check if not change the spark plugs.
Hmmmm.........I dont like the sounds of this white smoke, that is indicative of a headgasket leaking, or a warped head, and when it warms up it is expanding and then sealing..........the only way to determine this is to do a compression test when it is cold and then compare it to a compression test when it is warmed up.
Does it seem to be getting any easier to start, and running better?