Solar radiation peaks at the time of the summer solstice around the third week of June.
Here in the Northern Plains, summer temperatures are usually at their most consistently warm in July and early August. This lag is due to the retention of heat by and of water in particular. Water heats up more slowly but retains heat longer than air. This is why lake water temperatures are usually at their warmest near the end of summer.
This is also why hurricane season peaks in September. Ocean temperatures in the tropical Atlantic are at their warmest this time of year. This means evaporation rates are at their peak as well. High evaporation leads to high humidity, which turns to clouds and rain when tropical storm motions cause this humid air to rise. The energy released by the condensation of water on such a large scale is precisely what makes a hurricane such an energetic storm system.