Depends in Minnesota on where. Further north you go, the colder (duh!)
For the far north (near Canada) very late May and all of June, or September to early-October are the prime periods. I've had some cold (but not freezing) fishing trips up near International Falls the first week of June, but mostly 60-mid 70 degree days, with 40-50 degree nights. We've had very rare blizzards as early as Halloween in the Twin Cities, but usually late into October is great mid-state and south. This past two weeks near Bemidji (mid-north) it was great - lows around 50, highs in the mid-70's to 80. July is usually good all over, although getting warmer further south. August can get steamy - high humidity, temps 80-90 plus. Cooler up north.
Wisconsin would generally follow the same pattern. Close to the Great Lakes, things tend to moderate - not so hot, but not so cool, either.
The one year we went to Maine (Acadia) in May, it was about the same.
