underground thermal mass question?

Planning on building a strawbale house and attaching an underground greenhouse to the structure, trying to figure out if I should attach the greenhouse to the east/west side of the house or the south side. I was thinking that if it was dug directly south of the house that the sun would heat the ground under the house and it could act as a thermal mass. I'm in northern Ohio and we get pretty cold winters, any thoughts on possible benefits or drawbacks to this idea?

Nic,
That could possibly really work great!

You could use tubes under the home to carry excess heat from the greenhouse in summer under the home for storage.

I would think south side, but this isn't something that I have experience with, but I have been designing something similar and wanted to voice support.

Only dry earth will work as thermal mass.
Any water, whether from above or below will suck any heat right out. Look at your elevation (close to water table?) and the feasibility of putting an impermeable "umbrella"(and drainage) for 20 feet around your intended area if you want this to work.

Search for umbrella house or "passive annualized heat storage" for more details.