In the Slowing Down Series, which I will undoubtedly revisit to clarify points, I proposed a special case of condition equilibrium. Because of the massive amount of water on Earth, the heat of fusion and evaporation provide a range of temperature controls allowing the surface not only to be warmer than the amount of absorbed energy would imply, but to allow the Earth to maintain a warmer range of temperature for a much wider range of available energy than previously imagined.
The heat of fusion of salt water is approximately 271.5K degrees. In order to change phase from liquid to solid, the salt water much release more energy than require to just reduce the temperature one degree. The temperature of the freezing point of salt water and the enormous mass of salt water provides for conditional equilibrium controlled by the steady state energy required to balance the heat released during fusion.
The heat of fusion of fresh water is 273.15K. In order to change phase from solid to liquid, the fresh ice requires more energy be absorbed that just for the change of ice one degree. The temperature of the thawing point of fresh ice and the amount of absorption required provides for a conditional equilibrium set point dependent on the total available mass of fresh ice.
Since the 271.5K set point is dependent on the huge total available mass of liquid salt water, it is the more stable of the two set points. The 273.15K set point becomes dominate when the mass of fresh ice is sufficiently large. Under this control condition, the radiant energy of the ice plus the heat of fusion energy released determines the average temperature of the Earth. 315.6Wm-2 plus 6.07J/gram of ice melt in a season. Since the amount of energy provide to the Earth is limited by the Sun, the maximum energy available with current solar insolation is 1361.8Wm-2 which when divide by 4 to allow to the spherical shape of the Earth would be 368.08Wm-2. 368.08-315.6=52.4Wm-2 of energy released by fresh ice thawing for an average temperature of 283.8K or 12.53 C degrees as a conditional equilibrium temperature. This condition would have the greatest albedo impact which would likely result in less stable temperature control.
For the 271.5K set point the conditional equilibrium using the same solar value would be 368.8-306.9=61.9Wm-2 of energy gain required at a stable temperature of 283.8K degrees. With the albedo of liquid salt water being near zero, the system would easily exceed this requirement resulting in a higher average temperature. Without albedo feedback, the upper temperature would be limited by the heat of evaporation. Obviously, boiling would set a maximum temperature, but evaporated water would condense releasing the heat gained in evaporation imposing a limit below 100C.
The next step would be to narrow that range.