Is it smoke, or water vapor? Smoke tends to linger, while vapor dissipates. Any running issues?
I'd bet on water vapor too, particularly if it is white. Dissipation time depends on outside humidity level. (You got any humidity there is AZ, Scottly? Is it monsoon season?)
Anyway, get the entire engine and trans unit up to operating temperature and keep it there for 15-20 minutes. That's a rough guideline to ensure all the water has been vaporized and evaporated.
You may never get the far ends of the trans hot enough to convert all the water, while idling in the shop, or driving it leisurely around the block. And every time you cool it down, it will pull more humidity from the air and collect it inside the engine/trans.
Cheers,