People get this one wrong a lot in trivia games, incorrectly guessing midnight. Usually, the low temperature is recorded right around sunrise, often as the sky is already brightening.
The temperature keeps dropping through the overnight hours because there's no sunlight to add heat to the earth's surface. In fact, if the sun never rose again, the earth's surface temperature would continue dropping, perhaps to around zero degrees. The temperature usually doesn't start rising again until shortly after the sun comes up and begins warming us. The rare exception is when a mass of mild air is in place overnight and a cold front comes through later in the day. We've had days when the daily high occurs at 8am, thanks to a warm front's arrival, and then the low occurs at 5pm in the wake of a passing cold front. This is one of those rare upside down days you hear me talk about occasionally.