It sounds like having 2 thermometers might be helpful--one for the milk and one for the water. With two thermometers, you should have a good idea about what temperature your milk will eventually get to. After using 2 for a bit, you'll get accustomed to how much the milk temperature changes compared to how much the water temperature changes.
You can also calculate the final temperature before hand if you don't want to learn just through experience. If you think about the amount of water in your sink compared to the amount of milk in your pot, and the difference in temperature between the two, you should be able to control what happens with the milk temperature pretty well. For example, if you have a pot of 2 gallons of milk at 88F in a sink with 6 gallons of water at 100F and you stirred both the water and the milk until they were the same temperature, they'd both end up at (2*88 + 6*100)/ (2 + 6) = 97 F. How fast they get there depends on how fast you stir. Does that make sense?