Mud is porous (as long as you don't glaze it) and it has a pretty good R value. So it's the material more than the design, though anything approximating a sphere will do better than something with straight walls due to the maximum enclosed space within the minimum size skin. That also helps when you want to heat it. (Least heat transfer area to the outside.)

Why would being porous help, unless the mud is damp and there's some evaporative cooling going on?

I know in the American southwest adobe construction is popular, but that's about sheer thermal mass moderating the effects of the heat. Small windows also help.

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.

Mud houses in traditional cob and adobe designs tend to be built thick, partly in order to be sturdy, but also because the sheer mass of the walls acts like a heat capacitor that can be used to either absorb cool night temperatures and smooth the temperature extremes, or warmed with a constant low level fire for colder climes.

I believe the thermal mass for mud and adobe is higher than cinder block or stick frame buildings so the structure gets cooled in the night and remains cool throughout the day with the added benefit of providing some additional warmth in the night.

Ground coupling is another factor. I learned a lot visiting the Eco-Village Training Center in Tennessee in 101F (39C) heat. The cob house was as comfortable as the air-conditioned cabin.