Engine sputter

I have a 2002 Ford Taurus SEL 24 valve that was 100% flawless up until this morning when I started her up and she sputtered with the battery light lit.
The engine sounded like as if the choke would not release as it has been cold recently now that it's winter. It was running very rough and black smoke was spewing out the tailpipe the whole ordeal seemed so unreal and lasted 5 to 10 minutes. I went ahead and drove around the block and the car would accelerate up to 5 - 10 mph and then sputter and stall. At one point the car did stall and I put her in neutral and started her up again and everything was fine as if nothing had happened. The engine was running smooth again, all the power was back and the engine was already nearly heated up.
I called the dealership and they said the car has no choke, everything is regulated with the powertrain control module. They would check the codes but I don't think there are any codes as the check engine light has never turned on.
What is wrong with my car? What kind of trouble am I in now? The car is still under warranty as it is not anywhere near the 36,000 mile mark.
Could it be a sticking EGR valve? I have a pretty good idea about how these modern electronic engines work but I'm no expert at it. Gone are the days of distributers, points, rotors and carburetors.
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Unfortunately, this was an obvious anomaly and there probably wont be a code stored... if there was it would only confirm a too-rich condition.
Suspect you MIGHT have an Engine Coolant temp sensor or wiring to it going flaky.
Are you saying the battery lite stayed lit during the bad-run episode, then went out when you restarted?
Eastward Bound opined in

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Yes it went out after I restarted.
I have a VW beetle that does the same thing, it's battery light stays on sometimes when you start her up and for some reason the idle speed is too low. The light goes away after you step on the gas which turns the alternator faster to crank out more juice.
Yesterday the engine on my Taurus sputtered and it sounded as if I had some dead cylindars as if some of them weren't firing. The car would not accelerate under load and if you revved the engine in Park the engine would cut off at a certain RPM level. Black smoke and what looked like black charred liquid spewed out the tailpipe and made a mess on the driveway.
I post here to find out what is wrong with the car.
I will have a look at the coolant sensor contacts.
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FYI, the engine will be limited to ~3800 rpm when in park or neutral to protect from over-speeding the engine. The black smoke sounds like the bad carb on my Pinto - burning way too rich, although mine never spewed out any black goop.
I have noticed a few very minor anomalies with my '02 Duratec Taurus, but have learned to live with them. The most noticeable is the occasional 'sputter', like it's missing a spark every few hundred-thousand rpms or so.
I think I'd set up an appointment with the dealership for a check-up, being a major driveability issue, unless the problem seems to have gone away.
The question I would ask right now is: Has the problem repeated since then? Have you put more drive cycles on the car? If all seems well, I'd chalk it up as a hiccup. If it repeats, work the issue.
Good luck.

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