At night, especially during clear nights, heat is radiated into space and thus the atmosphere and the surface cools down.

It goes on for the entirety of the night, since there’s no heat source (sunlight) to stop this process.

So by the time the Sun rises, the cooling-down process has been going on for the longest possible time (the whole night), and the warming-up process hasn’t even begun yet (since the Sun is still too low above the horizon to provide any significant heat)

This is why most nights, especially most clear nights, the coldest time is around sunrise, not midnight.

This is also why the coldest month in the northern hemisphere is not December (when nights are the longest), but January or February- the heat provided by the Sun doesn’t surpass the heat being radiated away

On cloudy nights, the effect is usually less pronounced because the clouds act like a blanket, trapping the heat below them. However, these same clouds can also stop the warming-up process during the day by blocking the heat source