Stalling Saab 9-3 2001 2.0 turbo

In the work done recently you didn’t mention, spark plugs, air filter, throttle body cleaning, and some general “tune-up” types of items. Are they all maintained up to snuff recently?

If so I’d investigate the “cold” start system. Perhaps the computer is putting too much fuel in the mix thinking the car is cold when it is warmed up. That explains why it starts fine with it cools off.