How come my 1990 firebird will crank up but then warms up a little it cuts off?

A proper diagnosis needs carried out. If I'm looking at the car, I'm thinking about what changes when the engine reaches operating temperature. The amount of air needed inside the intake manifold definitely changes, which means I would look at restrictions of the air coming in. I would also look at vehicle exhaust to see if there are any exhaust restrictions. Lastly, when you reach proper operating temperature, your engine's computer goes into "closed loop" function, which means that it relies very much on all the sensors and inputs into the processor to vary fuel, air and spark mixture to run the vehicle properly. If anything is malfunctioning in the engine performance system in these areas, you could have a stalling issue. Which goes back to performing a diagnostic test to see what is going on when the problem occurs.