Hmm. I'm sticking with water-carbon life for the moment, and I can assume that evolution would work to maximize U. I suspect that the lifeforms in question would end up looking like cylinders stretching from the hot side to the cold side. I can't imagine any reason for increasing their surface area, just the surface in contact with the sides. A decreased overall surface area might help prevent losses, which would make them look like a soap bubble stretched between two circles of wire.
Did you mean that U is

or

? I can't quite tell from the way you phrased that.
I think that starting with the U for a column of water would give a likely upper bound. I don't think that water-carbon life will be able to exceed that without creating internal metal structures, which doesn't seem to happen anywhere on Earth. Does that sound reasonable?