I have a pair of 3.5hp B&S engines on push mowers. Both exhibit the same symptoms.
Engine starts and runs fine when cold.
Engine runs smooth at low and high throttle. (let it warm up for 10 mins)
Wont start again, any throttle position.
Once the engine cools down, start no problem
I have cleaaned the carbs, tanks, air filter, etc.
I did notice that the choke flap always closes, after the engines run, no matter how warm (or hot) they are.