That's a pretty interesting theory and makes sense when you break it down like that. If we think about the Earth's radiation budget, there is typically a net surplus closer to the equator and a net deficit closer to the Arctic region and in the essence of balance the net surplus equals the net deficit and boom...you have a balanced Earth energy budget...but with the idea of global warming this balance is probably not so balanced anymore. Anyways got a bit off topic but the idea I'm getting at is to what you were saying...theoretically if we're storing more energy during the diurnal cycle, for some sort of balance to be restored, just as much energy needs to be released in the radiative process.
What would be a super interesting study is taking a collection of nights where radiative cooling occurs and temperature readings at the lowest surface elevations within that area and then record temperatures at surrounding higher elevations. As we know with radiative cooling, lower elevations tend to be colder than higher elevations (resulting in an inversion). Just from observations, there seem to be times where the temperature gradient between a lower elevation and higher elevation could be pretty steep...you could essentially probably measure the "release" of radiation based off the temperature gradient