The water does not perform work in this instance.

I do not think you're trying to say the water "does work" in the physics sense, but to clarify, the water is just a large heat sink that has a much higher heat capacity than air. You can heat the water with air (which in turn cools the air), and that water can hold MANY times the heat (per unit mass) that the air can. Water also has a higher thermal conductivity than air. Allowing it to absorb and pass heat very well. This water is in the ground which also acts as a massive heatsink.

The air passes heat to the water which then passes the heat to the ground effectively cooling your air feed. A quick look online says current soil temp in Iran 21 inches deep is 35C or 95 F. That is your lower temperature limit. It's physically impossible to become colder than the soil temperature (in this instance, as that is your lower temperature bound for heat transfer, in reality you wont even get there, because your driving force for heat flow is gone at that point) without putting in mechanical work (which is what a compressor does in your air conditioner) to compress your cooling fluid so that it may be evaporated repeatedly to exploit the tranfer of heat into an evaporating substance