3.1 mega problem

[frankie_eh]

I have a 92/ 3.1 /RS cav./ automatic
301,000kms. on the old gal.
When it is first started, say in the morning (starts perfect first turn of key) BUT after approx. 1minute warming up... it just stops and won't start back up (almost like no gas is getting to it)
Note... I found that if you sit and "rev" it up (around 2000 rpm) right from the time it starts until it is hot (approx. 4-5 minutes)... all is okay and drives fine.
-Once it is hot, if you turn it off though... it won't start again until it is cooled right down (approx. 1hour). Then same thing... starts first try but unless you rev it up it will stall after approx. 1 minute.
-I can also start it and drive it right away. All is fine for about 1-2 minutes. Then right out of the blue the engine stops running and won't start again until cold.

Thoughts and suggestions required. (I've heard others with the chev 3.1 have similar problems)
Thanks to all in advance.