I should restate what I said: instead of "that's assuming the entire asteroid is at 290K", I mean, "except the insulation layer", which you need anyway to keep the near-surface area livable.
If you need 20 meters for that, then your living volume is 21 million cubic meters, or a reduction of about 20%.
That's not to say that there's no contribution. More that I believe the calculations from that linked-to page ignore the difficulties of differentiating between the internal heat (cooled through black-body radiation) from surface heat from the sun.
For example, from Stefan-Boltman, cooling goes as T * * 4, which means if you have a cooling radiator on the sun-side which is at 150C, or 20C above "normal", then it's about 6 times more effective than a -90C radiator on the cold side. I suspect it's easier to stop the 20C delta on the cold side than the warm side.