This sounds like it is running too lean; and the leanness doesn't become apparent until the engine heats up enough for the warm-up enrichment circuits to turn off. The possible causes of such a problem are 1> Throttle position sensor defective or improperly adjusted. 2> Fuel filter clogged. 3> Throttle body needs cleaning. 4> Clogged or dirty fuel injectors. 5> Leak in vacuum hose to MAP sensor, or defective MAP sensor. 6> Mass airflow sensor defective or needing cleaning. 7> Fuel pump or fuel injection pressure regulator defective. 8> Coolant temperature sensor for the fuel injection system defective: (There are two coolant temperature sensors on that car: The one with the single blade terminal is for the temperature gauge. The one with the brass body and rectangular black plastic two terminal plug is the one for the fuel injection system).
From what you described; I would think the fuel filter or the fuel injection coolant temperature sensor are the most likely causes of this problem. The third most likely cause would happen if the spark plug cables needed replacement. This is not a cause of leanness; but would come from weak ignition; which would be unable to ignite the fuel mixture after the engine reaches normal temperature and the richness from the warm-up mixture then leans out.
I also need to add that any modifications to the engine; like a cold air intake, header, low restriction exhaust system, or performance cam will cause the fuel mixture to go lean. And if the fuel system calibrations are not reset to match that modification (which requires specialized equipment and experience) this kind of problem could arise.
I hope this helps!!!