My 1600 has that problem, starting "hot." When starting "cold" it turns over without a hitch. But if I park it long enough to, say, fuel it, restarting is hard and I need to give it throttle to keep it from dying.
No word on whether this continues past 500 mile tuneup because I took it straight home from there.
The service tech at the dealer told me that the T-bird does not like ethanol and I should avoid higher-ethanol flavors of gas (and therefore, skip Holiday stations with their "blue earth" gas, which has a higher proprortion of ethanol). I was also advised to start fueling her up with mid-grade (89 octane) gasoline.
Incidental: I also seem to have a sticky speedometer when the temperature gets hot, but we'll see how that goes.
My ride: 2010 T-Bird
SO's ride: 2009 Can-Am Spyder