Imagine you are filling up a bucket that has a hole in it. As long as you are pouring water in it faster than it can leak out of the hole, the water level rises. As soon as you start pouring water in it slower than it leaks out of the hole, the water level goes down.
Heat is the same way. The summer solstice is the day of the year when you have the most sunlight being pumped into your hemisphere. But that doesn’t make it the hottest day, because all of the days after that still are pumping in a lot of heat. More than that part of your hemisphere is losing. So you actually tend to see the hottest days of the year in August in the northern hemisphere. After the summer solstice because the heat is still building up.
Same thing happens in reverse in the winter. The winter solstice is the day when the least heat is being put into the system, but the days following it still have very little heat being put into the system so it still gets colder and colder so you tend to get the coldest days in late January or early february.
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