I worked for hours stripping a carb for the same fault. It turned out to be the spark plug with the internal resistor to stop interference. The spark plug looked great on the outside but the resistor had gone. The engine ran for 15 to 30 seconds then stopped when it started to get hot. New spark plug cured it 100%. See if your plug has an R somewhere in its number or under the number.
Mart the Fart
August 2009
Most likely a blocked vent hole in the fuel cap. To test, remove it & allow to run. If it doesn't stop, problem proved.
New caps are about £3.50
phil_saunders(a)bigfoot.com
Phil Saunders
July 2009
Automatic Answer
We may have found other answers which could help you.