To answer the original question, it’s because the earth is very large and retains the heat from warmer times preceding the solstice in the water bodies and the ground, like a buffer, so there is a lag time for things to lose that heat and get to the coldest air temps. As an analogy, if you heat up some rocks in the oven, then turn off the oven, the rocks will still stay hot for a long time and gradually cool off.