I hook it up to an external 1920x1080 display, with the internal open.
Me too, 90% of the time my MBA is on my desktop connected to an old 23" 1920x1200 Apple Cinema Display. I keep the lid open and the internal display brightness cranked all the way down most of the time. When I run the external display with the lid closed (clamshell mode), the fan kicks into high gear too often.