I had this problem on a different mower. It was the spark plug!! It starts fine when cold but some plugs have a built in resistor to stop TV interference and this is the problem. The resistor craps out when warm and the engine dies not to start again until cool. Worth a thought - sorry I don't know about the mixture. I've had a B&Stratton Mirage for donkey's years and never needed to touch the mixture.
Mart the Fart, March 2009