If you don't have an air box, what do you have? A lot of us have removed the air box in favor of a free flow filter. Here is mine:
http://scootdawg.net/album.php?albumid=92&pictureid=551
When this is done, the carb needs to be rejetted, more air means it needs more fuel, or it will run way to lean, which in turn means to hot.
Running your scoot with no air filter what so ever, will cause an extremely lean condition, and hard starting, not to mention that sucking in unfiltered air, will destroy your engine.
You need to spend some time educating yourself on the gy6 engine. There are videos on youtube, covering everything you'd ever want to know about these engines.