I have the same as you.
When my car is cold it will start right up, but during the first 5 or so seconds of running, I cannot throttle up too much because it will run very uneven.
When the engine is warm, it starts difficult, except when it has sat for only a few minutes (see below). If I then let the fuel pump buzz for a while before trying to start (say, 4 to 5 seconds) then it starts pretty quick, although not quite as fast as with the cold start. As Hauser points out, the owner's manual advises to floor the pedal when starting the engine warm but I have not found this to make a discernable difference.
If my car has sat for only a few minutes or less with a warm engine (e.g. after fueling, which as we all know is a frequent event), it will start immediately!
So this is the strange part:
engine cold: immediate start;
engine very warm and sitting very short: immediate start
engine warm, but sat for 15 minutes up to several hours: difficult start.
It seems to me that, as far as the cause for all of this, the pressure in the whole fuel delivery system slowly goes down after driving which, on a cold engine, is compensated for by all the extra fuel injected through the CSV and the cold start thermostat on the FI pump. When the engine is warm, there is less extra fuel.
Of course I could be wrong, but it would be great to get the solution to this very common 'hard warm start' problem since so many seem to experience it.
Cees Klumper in Amsterdam
'69 white 280 SL automatic