Just to add to saturn tech, I had many of these and re built many of these carbs for this exact issue. The plugs in the bottom of the carb center body leak and make it real hard to re start when hot.
You need an old timer in the business that can verify this and rebuild the carb for you.
The converter may be damaged from this and I would still pursue this as well.
Tuesday, March 13th, 2012 AT 2:08 AM