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The Sun is the ultimate source of all energy driving the Earth's climate. But in part, it uses the atmosphere as its medium of energy transfer with the hydrosphere.

The hydrosphere of Earth is in a balance with solar energy, atmospheric gas and water in all it's states. It's the warmth or coolness of the air that interacts with water to melt or crystallize it. Direct radiative transfer of solar energy (such as sublimation of ice and snow or evaporation of liquid water) is a secondary mechanism of state change. Water can occur in solid and liquid form; if the liquid is put into solution with the atmosphere, it becomes a vaporous gas (NOT the same as steam, the true vapor phase form of water). By the way, water vapor (more accurately described as liquid water in gas solution) is a more powerful greenhouse gas than CO₂, yet is almost never accounted for in climate computer "models".

Isn’t this insignificant to the heat that was previously provided by the sun?

Investigating the Effects of Infrared Sky Radiation on Air Temperature

I'm sure that you have noticed how much colder a cloudless winter night is than one with cloud cover. I believe that Dr. Spenser lives in Huntsville, AL. If he had done this experiment in a desert area, the night time temperature drop would have been even greater.

The following is from way down the page:
"Why Was the Cavity Colder than the Outside Air Temperature? The temperature of virtually anything is the result of a balance between (1) energy gained and (2) energy lost. As long as the energy gained exceeds that lost, the temperature will rise. This was clearly seen when I closed up The Box, and the rate of sunlight absorption in the cavity exceeded the rate of energy lost by infrared emission (and any — hopefully small — conductive losses). The temperature skyrocketed.

But once the rate of energy loss exceeds that gained, then the temperature will fall, as was seen when The Box entered the shade. Then, then rate of IR energy lost (which increases rapidly with temperature) exceeded that gained from diffuse solar radiation, and the cavity temperature fell.

So, at night when there is no solar energy available, what is to prevent the cavity from getting very cold? Outer space is supposed to emit near absolute zero, 3 K. The Box’s cavity enters the hours of darkness at something like 300 K temperature. At 300 K, and assuming an IR emissivity of 0.99, the cavity is emitting IR at a rate of just over 400 Watts per sq. meter. Assuming the box is very well insulated, and is not leaking air, what is to prevent the cavity temperature from dropping well below freezing (273 K)?"