Can't tell for sure, but it might be some temperature sensor issue.
This engine doesn't have one.
Can you hear the external air injection pump running while cold?
This pump is injecting additional air while cold, to fake a lean condition so the e-gas is adjusting to richer.
Some other poster had a slipping belt, if so it could reduce the additional air injection.
Still, this is probably not the problem....
Have a look if the electrical clutch is engaged, only when cold.
There is a AIT (Air Intake Temperature Sensor) at the crossover duct on the driver side.
It's basically a Therrmistor that measurs the Air Intake Temperature!
Also, there is a engine coolant temperature sensor for the computer, at the thermostat housing, could be sending wrong values.
The MAS (Mass Air Sensor) would be another one, but if it was defective the engine would run all the time crappy.
Of course the is the fuel pump itself and related as TnBob already mentioned.
And, aaah ye olde code reader or this one should have an OBDII, this would give you a pretty good idea what is going on!