The next night some clouds roll in, the humidity climbs a few points. Heat collected from solar radiation during the day in the rocks, soil, concrete and asphalt of the surface radiates from the surface but before reaching space is absorbed by the water vapor molecules in the air. Each molecule heats slightly until it re-radiates in a random direction. Half goes up half goes down. It make take several steps to get to space. It takes longer for the heat to be eliminated. The surface temperature is warmer.

During the day it's a tale of two frequencies. The frequency of radiation is proportional to the temperature of the radiating body. The hot sun produces high frequency radiation. We see visible light, but there is also plenty of infrared and ultraviolet. At night the radiating body is the surface of the earth. It is much cooler than the sun thus radiates only at the lower frequencies, predominately in the infrared.

We are used to air being transparent to light. Fog interferes with transparency of visible light but dry air, including water vapor (not condensing fog), and greenhouse gases like CO2 and methane are transparent to visible light. It turns out that infrared radiation gets absorbed and reradiated by gaseous H2O, CO2 and methane (CH4). In a spectrometer analysis you see several absorption bands for each of these gases in the IR frequency range.

So yes blanketing works. It is intuitive.  Meteorologists talk about it every time there is an unusually cold, clear night.