Of course, Sun is our supplier of heat. But the thing is, he doesn't supply it to us directly. The heat (or temperature, loosely) we feel normally is that of the lower atmosphere in contact with the earth's surface. This heat is not the same heat coming from Sun. The energy coming from Sun, when it reaches earth's surface contains majorly visible light which does not have heat content. Our lower atmosphere (or the gases present there) cannot interact with this visible light. Our earth absorbs this heat and gets heated up. Then earth begins to give out this energy in form of longer wavelength radiation called Infra Red (IR) radiation (When you are near a fireside, visible radiation is what you call 'the light' and IR radiation is its warmth). The gases in the lower atmosphere including water vapor and carbon dioxide can absorb this IR radiation and that is what we feel as atmospheric temperature. In short, it is not Sun that gives the warmth we feel, but the Earth. In day time, our Earth stays taking in and giving out radiations, keeping a balance. But during night time there is no taking in, but only giving out. It is this given out heat by Earth that keeps us warm during nights. Otherwise we would have all gone frozen to death. Earth keeps on giving out heat energy without any intake of energy until the Sun shows up again. Now you can guess what happens just before sunrise no? Earth has lost maximum of its energy content and that is why dawn is the coldest of all time. Now it is also clear why isn't midnight the coldest of all hours. Because at midnight, the heat loss from earth is only half along its way to dawn.
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