see if you can find teh manual here.
http://www.suzukiinfo.com/and study the carburetta bit very carefully....sounds like you need to adjust the hot idle.
im trying to sort out the idle on my g13a, its got a fairly complex hot/cold setup, which i suspect yours has too. I have the opposite problem, where it wont idle when its cold unless i turn up the idle screw, then it idles fine cold, but when it gets hot where it idles too high!
Im almost to the point of putting a cable in to pull on the choke lever manually....