I phrased this wrongly and want to be perfectly clear: the warming effect in a greenhouse is entirely due to the greenhouse, not the gases inside it. The action is mechanical, blocking heat exchange mechanisms taking place, mostly convection. In the atmosphere, similar mechanical action is done by clouds. Hence, all else being equal, a cloudy night will be warmer than a clear night.
What we call greenhouse gases are no more than weak temperature regulators, delaying heat transfer as they absorb and re-emit IR radiation. In the case of CO2 the effect is negligible, in the case of water vapor it is more pronounced and measurable. In a greenhouse, the delay action will serve to reduce temperature extremes but will not affect the average. All else being equal, a dry greenhouse will have the same average temperature as a damp one.
Whether this delaying action will have any influence in the open atmosphere is doubtful as the gas is free to take part in the usual heat exchange. Theoretically at least, we may say that the gas will keep the night a little warmer (delaying and reflecting outgoing radiation from the Earth) and the day a little cooler (delaying and reflecting incoming radiation from the Sun).
To be clear: greenhouse gases have no effect on average temperature over the course of a day and probably no effect of any kind on the atmosphere.
I urge the reader to investigate the physics of my argument to confirm it is correct and use the knowledge in the fight against the fraudsters.