I have a high tunnel, and don't want to go to the expense of installing an automatic vent opener. Could I just add so much thermal mass that all the extra heat is absorbed? Or would this not be physically practical?
I think not possible. In my Colorado greenhouse, heat buildup in the summer is the biggest extreme of climate. Without ample venating (emphasis on ample), your plants will be severely heat stressed, if not cooked outright. I would say that planning the ventilation is a more important consideration than the heat retention. I would suggest two vents, to allow cross-ventilation. You will not regret having too much ventilation.
A greenhouse cools down slowly, but it heats up really fast. Plants do not like sudden temp changes, hot or cold. When your greenhouse is 65 degrees in the morning, and then heats up to 120 by 10am in the direct sun, your plants will suffer profoundly.
Thermal mass is simply not going to be able to absorb that kind of temperature change rapidly enough to matter. Even with a sophisticated 'climate battery', like Jerome uses at CRMPI, I think you are going to need vents for the sunniest days of the year. His greenhouses all certainly have external vents in addition to climate batteries.
What Adam says sounds right to me, unless you're talking about winter only. In winter, you mebbe can get away with no, or very little venting. Our solar growhole is sorta dug into a hillside, and requires only a bit of venting in winter. We're close to St. Louis, so in summer, we don't raise anything in there... Too hot!
Used to be, there were these gizmos that would open and close vents w/o electric. Never seen one up close, but that would be something to look into...
I had a 6'x8' greenhouse kit at my old house in N Colo. Even with the door open and an automatic vent, the temps were approaching 145f in the day during June. I had to string out an extension cord and mount a box fan attached to a timer.
It was a bit of hassle, but the greenhouse was useless without it.