I know the Charcoal canister and how it can affect the gt's has been addressed, however I'm having the same problem but the canister has been disconnected. It seems that when the scooter is warmed up and left to sit for approximately 20-30 minutes, it starts hard and continues to stall. At the first service, the dealer disconnected the canister vacuum line but the problem persisted. Two weeks ago, I went riding on a fairly warm day, 60's, and the same problem. It sat for about 20 minutes or so and then refused to idle. I had to ride the scoot home with the accelerator and the brake so it wouldn't stall. When I parked it in garage, it reeked of gas and I heard a persistent clicking sound similar to what a electric fuel pump. Does the gt200 have an electric fuel pump?
Anyway, it didn't start all the afternoon or the next morning. The dealer had it towed to their shop. They reconnected a loose vacuum hose, the one they disconnected for the canister in the first place and did some carb adjustments. When I got it home, it seemed ok but the idle in my opinion seemed a bit too high. It also backfired every so often.
Yesterday, about 70 degrees here in Denver, I rode it about 10 miles and stopped. It started ok after a 15 minute stop. I should mention also that since the carb adjust, it does have an intermittent exhaust popping. I rode about another 10 miles and stopped for about 20 minutes. Guess what? Right!. Started hard! Stalled a few times but since the idle was a bit higher, I did manage to make it home. Once in the garage, again it reeked of gasoline, and that clicking sound continued for about an hour after I shut it down. It wouldn't stay running for the rest of the day.
Since it did start this morning, I took the bike today back to the shop, shut it down and it started fine. They couldn't duplicate the problem this time. I'm at a loss. I think it sounds like a bad electric fuel pump, but was told they didn't think it had one.
It's a 2006 with 1100 miles, close to 200 of those just going back and forth to the dealer for this problem.