Ok I know it has been a while since we were talking about this but I got some readings today in the Texas heat. It was 102 in the shade near the rabbitry and 82 in the rabbits underground boxes. So far I am pretty pleased.
Why are you insulating them from the cool temperatures of the ground? The rabbits need to be in contact with the thermal mass of the ground to get the greatest effect.
velacreations - You guys are probably in a very different climate than us. We did basically the same thing you did except your boxes are made out of bricks. We have a brick structure similar to one of your boxes, but it is used as an oven. We get lots of sunshine and triple digit temps. The bricks radiate heat and make a wonderful outdoor oven. Of course you can also bake cookies on your dashboard and fry an egg on a rock, so building the oven was kind of unnecessary here - . It looks cool sitting next to the firepit though. Also it looks like your set up was inside a barn which cuts the sunlight issue for you. We could not put it inside a barn. It is out in the open and literally gets zero shade except for the cover over the box lids.
If we had used bricks to make the boxes, we still would have needed to cover the entire thing with dirt to keep the sun from heating them up. And then we would have still needed to use landscape timbers or something around that to contain the pile of dirt to keep it from washing away on the rare occasion that we get a torential rain. We used landscape timbers to contain the dirt as they don't radiate as much heat as concrete or bricks. Then it is sitting on the ground and filled with dirt like a raised flower bed. Then the boxes are set inside that dirt insulation. They maintain pretty consistently comfortable temps for most of the year. In summer we put an ice bottle in the insulated box each morning to help drop the temp down a bit more. That may sound like a pain, but it is nothing compared to other rabbit owners in the southwest that have posted about needing to change ice bottles several times a day and check the rabbits every hour. Many are losing rabbits due to heat despite having them under shade with misters and fans. It is just a really rough climate here.
On the ciheam link I think that would be great too. But here we have snakes and fire ants so putting something down in the ground makes it harder to keep those out and harder for us to clean out and tend to as we are kind of old and don't bend or squat down as easily as we used to.
Both yours and the ciheam look like awesome set ups. We just had to do a few things a little different to deal with our crazy climate and the creepy crawlies that we have.