Does the cold start injector have anything to do with the engine after it runs?? I notice after my car sits over night in the cold weather of NY it run's funny. The idle bounce's and is low.if I rev the car a few times it seem to fix it self. Also it will stall untill the cars run's maybe about a min. though maybe head or intake gasket but I haven't noticed any lose of coolant. Could it be the IAC?? I replaced the coolant temp sensor. And have check the TPS. What do you guys think. Could it be an O2 sensor??

 

I'm no expert on the TPI system, but the ECM shouldn't be looking at the O2 sensor until the engine has warmed up a bit more than what you describe.

I think cleaning the IAC and throttle body out would be a good start, if it's gummed up the cold idle can be affected.