Starting with the majority of the Earth's surface, the oceans. and including the moist air envelope in the atmosphere that results from the liquid of the oceans, you find that the average temperature of the sea surface temperature (SST) is limited to a very tight range of temperatures. The true average SST would range from 21 C to 22.5C with a rather small margin of error. The average is limited because the freezing point of fresh and salt water ranges from -1.9C to 0C at surface atmospheric pressures and the rate of evaporation at sea level would have to closely match the rate of freezing if the oceans are to exist. So how does tight range allow for changes in the Global Average Temperature (GAT)?
If there were no land mass on Earth, the expansion and contraction of ice area would be the impact on the GAT, With the SST limited to the tight range by the thermodynamic properties of water at sea level, the energy emitted by the sea surface would be fixed at 425Wm-2 +/-20 say, the total energy available from the sun on average is 340Wm-2, so the total energy leaving the Earth would have to be 340Wm-2. 425-340=85Wm-2, so the average energy leaving the non-liquid portion of the Earth's surface and/or atmosphere would have to be 85Wm-2 on average. No fuss, no muss, 85Wm-2 period end of conversation. Since the total energy available is 340Wm-2, the non-liquid portion has to emit 85Wm-2, 240-85=155Wm-2, kinda scary right? That is the Aqua effect, not to be confused with the Greenhouse Effect. The requirement of conservation of energy, Ein=Eout and conservation of water, the primary thermal mass of the surface, specify very tight limits on the range of possibilities.
As the area of the true liquid sea surface expands, the area of non-liquid surface decreases which requires more reflective surface, clouds in the atmosphere provided by our sponsor, Aqua not so pura, meaning cloud albedo is a required feed back, not an optional feed back. On a true water world with no land mass, the habitable portion of the surface, the not frozen part, would be about 21.5 C plus or minus a touch on average. The "average" surface temperature would depend on the percentage of cloud cover, but the "average" temperature of the non-liquid surface would range from -76.4C (85Wm-2) to 0C (316Wm-2).
So the "Average" surface temperature is fairly meaningless since only the surface inside of the moist air boundary is critical for the the energy balance. Any surface at or below -76.4C is not a part of the surface average, but a response to the overall conservation of energy requirement. Concentrating on the moisture boundary and the relatively minor radiant boundary will prove that the "Faint Sun Paradox", is not a paradox, but a misunderstanding of basis thermodynamics.