2nd law of thermodynamics and net heat transfer

Just received a very interesting email regarding the 2nd law of thermodynamics and net heat transfer with respect to the Desert Fridge:

Foaad: My initial impression is that the assumption of net heat transfer in steady state is incorrect as it would imply constant cooling without limit. Also it seems to violate the 2nd law of thermodynamics that heat transfer from lower to higher temperature is not possible without input of work. I think by making net heat transfer zero, we can calculate the minimum temperature possible based upon outside temperature and humidity. In such a case any heat transfer caused by the temperature difference would be resulting in evaporation only.

Qasid: I agree that there would initially be an unsteady state heat transfer process occurring in the DF as water begins to evaporate and draw away heat from air inside the inside pot and thus gradually reducing the temperature of the air inside the inner pot and thus setting up an increasing temperature gradient and therefore driving an increasing rate of heat transfer from the constantly hot surrounding air to the cooling air insider the inner pot. Ceteris paribus, this system would eventually reach a balance between these two competing heat transfer processes (reference) and therefore we would not have infinite constant cooling

Regarding the second law of dynamics, it is proposed that the refrigeration process is maintained by the heat carried by the molecules of evaporating water (reference:Dr Ataul Habib Khalid). It is the same method whereby we can cool our bodies even when the surrounding temperature is hotter than our core body temperature (reference).

If we assume the net rate of heat transfer is zero then, by newtons law of cooling, this suggest there is no temperature difference between the surroundings and inside Desert Fridge.