[Reeses]

The heat radiates out because the clouds aren’t retaining the surface heat.

Clouds reflect the surface heat back down, and sunshine back up. It does not matter to the surface what the heat content of a cloud is, only it's thickness and altitude. Blankets don't keep you warm by being warm, but by reflecting your own heat back at you. Due to its inefficiency, a blanket becomes slightly warm from your heat loss, but that has no influence on how warm it keeps you.

[allmost]

This not complicated. The higher energy wavelengths penetrate the cloud cover. The lower energy, longer wavelengths do not penetrate as easily. The higher energies penetrate, interact with surface materials and radiate lower energies such as the color spectrum or infrared. These are blocked by the clouds and absorbed by ambient atmospheric moisture. The heat is retained on the earth's surface for that reason. Deserts often vary widely in night and daytime surface temperature for this reason. The water vapor holds the heat. That's why when we build a coal or nuclear plant they are run on steam. Water's ability to store heat energy is converted to mechanical energy through turbines.