How wide a hole to still benefit from geothermal radiation?

I've seen some semi-buried greenhouse on youtube. Dig down 2-3 feet and you get a little bit of warmth radiated back from below grade soil.

At what width does this not work? I saw someone post a comment that wider than 15ft hold you wouldn't benefit much from below ground radiation. I hadn't thought about that before.

Any thoughts on this? I know some underground greenhouses (like ott kim) are wider than 15ft.

Can you give more details about the concept?
Are you talking about frozen soil, desert or temperate areas?

The quality of greenhouse is a huge variable. For the excavated area, the ratio of depth / surface area probably has a magic number that is just right for whatever latitude. I think a good starting point for figuring this out is looking up the maximum frost depth for your area.

A government entity where I live was promoting half-buried greenhouses for a while. We tried it and abandoned it after the first winter. The south wall cast a long shadow in midwinter, but we get a lot of solar gain so that was a major loss. Also we had to peel away a corner off the top and climb down in to maintain, water o r harvest, which of course isn't good for retaining heat.

If your region has very little solar gain in midwinter it might be worth it, I don't know. At very north latitudes the shadow would be even longer though.

Thanks for the replies.
Latitude 34 degrees, north Georgia zone 7b, almost at top of hill heavy red clay soil. According to older maps frost line is 12 inches but I imagine that is rare or out of date, would guess a lot shallower now.

What sparked my interest was this post:
http://www.bananas.org/f2/my-semi-pit-banana-greenhouse-18518.html

He claims to have kept above freezing just going down a few feet.