Why is the sunshine time getting shorter and hotter in the northern hemisphere after the summer solstice?

This doesn't need geography, this uses physics, and you can understand the area where you live as a very large overall environment. In addition to air, this environment also has water and the earth. These things have a large specific heat because of their large size. Therefore, when they are heated, they will not reach the highest temperature at once, but will rise very slowly. Therefore, although it is difficult for the sun to move directly, the temperature in the northern hemisphere has not reached the highest temperature at this time, but it will continue to rise slowly with the passage of time until a critical point, that is, the local temperature situation reaches the maximum heating capacity that decreases continuously after moving directly south, and then the temperature will gradually decrease.

You can understand it with a temperature gradient of one day. Usually the sun shines directly at 12, but the temperature is not the highest. Generally, the highest temperature is around 2 o'clock, as above. It's not bad to describe it with physical inertia.