I have an Asus laptop too small to read running a larger monitor. I want to put the laptop in a nearby drawer and close the laptop lid while still using the monitor. I am aware of heating. Can I do this? If not can I leave the lid ajar? How ajar is ajar?
You should just deactive the sleep mode in Windows when you close the lid.
It's somewhere in "Control Panel" with the name Power management or Power Options depend on the Windows version that you use.
In Windows 7-8 it's Power Options -> Choose what closing the lid does or in Change advanced power settings - Powe buttons and lid.