The most common problem with a TW that has been "sitting for a while" is a gummed up/dirty carburetor.
The easiest thing to try is to add a double dose (4oz.) of Seafoam to a full tank of gas. Then run the bike, then let it sit, then repeat. It takes a while for this to work. If you are lucky, the engine will run better, more smoothly.
If you are not lucky, you will get to learn a lot about the internal workings of your carb...or you will need to get a shop to clean it for you.
Removing the cap covering the pilot screw, and fine tuning the pilot screw/circuit will help reduce the warm up time. There's more.......
Download the Owner's Manual and Repair Manual:
Idle Speed Adjustment: Chapter 3, page 6 of the Repair Manual.
Start reading some of the info in the Tech WriteUps.
Yamaha considers your engine "broken in" (poor choice of words) by 600 miles. Synthetic is OK as long as it is "motorcycle specific" ....... Please no oil discussions.....