It is a familiar refrain from forecasters in spring and early summer: "cooler near the lake", or "warmer inland". Either way, it leaves many people wondering if they live lakeside or inland. The answer is not obvious because it changes with different weather conditions.
Anytime a component of the wind is from the east, i.e. northeast, east, or southeast, we will feel cooling lakeside due to the cooler water temperature compared to the warmer land (in spring and early summer). Water has a large heat capacity. It takes a lot of warm air and sunshine to warm the water temperature. So for most of the summer Lake Michigan retains the chill from the cold winter months.
Land, on the other hand, warms quickly. A sunny day with no snow on the ground can warm nicely. With two different masses (land vs. water) warming at different rates, there is bound to be a large lakeside to inland temperature difference.
The key to how far inland is "inland" is twofold: (1) the speed of the wind; (2) the wind direction. It makes sense that a faster speed wind will propel air parcels farther inland compared to a slower speed wind. As for wind direction, keep in mind that Lake Michigan is a predominantly north-south oriented lake. If the wind is nearly north or perhaps northeast, air parcels are traveling down almost the entire length of the lake before reaching us. They are picking up a lot of cold air along the way as they pass over the chilly lake surface.
An east or southeast wind has a shorter "fetch", or path, over the water. Therefore these wind directions tend to produce less chilly air. Northeast wind has a chance to build up a lot of momentum because the air parcels are passing over flat water surface with little friction. East or southeast wind carries parcels over less flat surface.
The bottom line: a northeast wind direction will tend to be colder and tend to be higher speed, so the chill is carried inland a greater distance. With a brisk northeast wind, it can be 40 degrees along the lakeshore this time of year and perhaps only as warm as 45 degrees west of Waukesha. A southeast wind could produce a 40/50 lakeside/inland split. A light wind from the east - southeast, e.g. 10 miles per hour or less, could yield a 43/60 lakeside/inland split this time of year.
It is helpful if forecasters specifically name towns or cities when giving a lakeside/inland forecast split. I will often say something like "a high of 40 is expected along the lakeshore but up to 55 degrees in West Bend, Waukesha, Burlington and areas to the west."