There always is some evaporative cooling going on. At night the cooling causes condensation, and the dry clay absorbs this moisture, then during the day sun and wind dry it out again causing evaporative cooling. How big this effect is varies in different climates, but from personal experience (I've helped build some adobe houses, and have friends who live in them) I can say that it's not negligible. Another benefit is that in humid climates (like mine) the interior of an adobe house tends to be significantly less damp; enough so that we can see the difference with the salt in the salt shaker... around here in brick/cement houses it always clumps very quickly, in adobe homes it remains lose and powdery (salt starts to clump when humidity is above 75%).

Yes, it is evaporative cooling. That's why I mentioned the pores. The mud wets and then later the moisture evaporates drawing energy from the surrounding clay.

Phase change can get you below zero easily, it certainly works as a poor man's AC. It is incredible how much energy phase change requires compared to just raising the temperature of the medium.