I had cold startup issues before (probably bad AAR) but that seems to be much better now. I now have a problem starting when warm. If I drive the car for a while, stop it for a short while (<30 mins so engine stays warm) it will start fine but the RPMs will drop in a few seconds and I need to give it a bit of gas to keep it running. Once I'm driving and if I stop the car at a stop light no problems and it will idle fine. I'm thinking the cold start injector may be staying on too long when warm and this would cause a warm engine to die. Does this make sense? It runs fine all other times. I'm thinking I could disconnect the plug for the cold air injector at warm engine startup time and see if this fixes it to confirm my issue.

Could be a vacume leak or might be electrical. You can start by determining what is NOT the problem. Sure about fuel? Sure about spark? I would use starting fluid all over suspect areas to eliminate vacume leaks. They're a killer.

The sensor in the coolant "T" and it's connector are a common source of intermittent problems. The sensor is a variable resistor and the resistance between terminals should decrease as engine warms up. 14 deg. F = 7,000-11,000 ohms
68 deg. F = 2100-2900 ohms and 176 deg. F = 270-300 ohms. So you can see an intermittent of poor connector would make the FI computer think the engine wants a richer fuel mixture.