I would assume your always going to have at least 2-3 degrees difference once you get a short distance into the *lake*. I am sure the difference is far more drastic when the temps plummet fast. I wouldnt be shocked to see the temp diferrence of 5 degrees or more by the time you hit the bridge in a extreme cold snap. The river upstream cools much quicker, not a lot of water up there. The lake on teh other hand is a massive body of ater that takes some time to cool.
The fall turnover is happening right now.. pretty soon we can throw the temp out the window because th surface everywhere is going to read 39 degrees… and go downhill from tere.