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Just buying a car it has cold start up idle issues until warmed up.

The owner is passing this of as an O2 sensor issue , I'm sceptical, high fuel usage and maybe slightly poor running hot or cold is my experiance with rooted 02 sensors , not over reving no power and crap idle which all goes away when warmed up that he's describing.

would a craped out O2 sensor cause the symptoms he describes ?

Coolent temp sensor.

Pretty unlikely to be the O2 sensor. Each model has a different setup for cold running, so hard to say what it might be but it's most likely in temp sensors or idle control somewhere. Get some more knocked off the price. The systems are not that complicated if you can understand these things and there's plenty of help on this forum.