Earth is often touted as both mass and insulation an isn't very good as either. Before the availability of closed cell foam and other great performing insulation, a pit greenhouse made a lot of sense compared to a Victorian iron and glass.
Earth sheltered might make sense today if you were building on a south facing slope, but otherwise, not, unless you own a backhoe and enjoy excavating.
The soil temperature isn't stable at 6 feet, it's more like 12 feet here in AZ. I'm near Concho, at 5600 feet. Our soil temp is 63+-2 degrees at 10 foot by my measurement.
Just saying you can easily insulate N, E, W walls to way beyond the performance of cold wet dirt.
It's the glazing losses that will do you in, thermally, and that's the same for pit or above ground.
Pity there aren't more good designs for insulating shutters, curtains, blankets out there.
