Becareful running the lines under the carpet, they still will have condensation and in the summer may get mildew in your carpet under there. Just a thought.
I can see that as being a concern for some. I'm in Utah where the air is very dry. So whatever condensation there would be, would dry very quickly. This might be the case with externally mounted lines as well. It might be a non-issue for me here.
Why not put lines underneath the car? I assume you are concerned about absorbing heat from the external environment.
Heat absorption is my main concern. I'll look more into it before I decide though. Maybe just a good insulation on the lines is all I need.