Coolant temp sensor is cheap and easy to replace. If it's bad, it tells PCM wrong info about engine temp, so if it's saying "engine is warmed up" them PCM starts listening to all other sensors to adjust fuel trim. But since the engine is NOT warm, those sensors give abnormal readings, causing it to run badly. When engine warms up, since the sensor already is telling PCM it's warm, then it runs normally.
Mind you, this is just an idea, I could be completely off the track here. But since CTS is a few bucks only, I'd give it a try...
Beauty is in the eye of the beer holder
* 1994 ZJ (by VIN) with a 1995 engine (PO knows why)