My Macbook Air 2010 11in overheats when I close the lid and run an external monitor
Just because the fan starts running faster does not mean that the machine is overheated.

If you really want to, you can open the Air's lid after the external monitor is connected. The Air's screen will stay off but the machine should stay cooler and not have to run the fans at a high speed.

Apple even has a knowledge base article for "clamshell mode".