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My prediction: we're going to invent alien intelligences on this planet a long time before we find them in outer space.
I think the weight of the ice would an interesting point to consider in these models. Glaciers definitely deform a planet's crust. The Great Lakes region lies in a depression that is still rebounding from the last ice age.

Reading this, my first thought on the "hot eyeball" would be that the massive ice cap would cause a depression on the night side. So no rivers would want to flow to the day side. Then I remembered a study regarding icecaps melting actually lowering the local sea level [1]. Since the ice is so massive, it actually attracts the sea locally with its gravitational pull. So when the ice melts, the pull is released, and the sea level lowers locally. So with the oversize icecap on the night side, it would attract water to it, even further preventing it from flowing to the day side.

http://www.sciencemag.org/news/2016/02/how-melting-ice-sheet...

Fascinating! I wish I had studied some geology. I learned here https://www.youtube.com/watch?v=oSSxdogrv1s that the mountains and lakes around Puget Sound run north-south because of glacial descent, and that the huge boulders we find scattered about the area are called 'erratics' as they were moved here by glaciers. I show everyone I can that video but I just get weird looks.

I wished the article had fleshed out the ramifications of the ice cap a little better.

There's another type that they're missing. Given enough water and ice on the planet, a hot planet could have a full ocean that is continually boiling on one side and raining/snowing on the other, with little or no islands poking out of the ocean.