Hyundai Repair: Rough idle when cold, coolant temperature sensor, hyundai santa fe

Question
QUESTION: I have a 2001 Hyundai Santa Fe 4 cylinder.  I love the vehicle and I only have 47000 miles on it. I live in upstate new york so it gets pretty cold up here in the winter.  So my question to you is, when it is cold and I start my santa fe up to warm up, it will idle extremely rough, and blow black smoke and soot out the exhaust so much so I have a big pile of black in the snow.  Once the car is warmed up all the problems go away.  I mean when it idles rough you almost have to put your foot on the gas to keep it from stalling.  I love this car and it has been very good, but this issue concerns me.  A friend said to change my thermostat and some temperature sensing thing.  If this is true where is the temp thing? And does this sound like the possible problem?
Thank you very much
Greg
ANSWER: The thermostat is certainly not the issue since it merely controls the flow of coolant.  Cold coolant which flows and cold coolant which does not flow are both the same in the eyes of the engine control module (ECM) at the time of initial start.

The coolant temperature sensor, on the other hand is a decent guess as to what may be the cause of your problem.  Since it only occurs when cold, it's possible that the sensor may be reporting the wrong temperature to the ECM, resulting in the ECM misadjusting the fuel mixture.  Normally, however, issues with the coolant temperature sensor result in the check engine lamp being turned on.  If the lamp is indeed on, you should start with reading the stored diagnostic trouble codes.  This will tell you what sort of problem the ECM has encountered.

---------- FOLLOW-UP ----------

QUESTION: Thank you very much for clearing that up, although the check engine light has only come on one time since we have owned the vehicle and it was for a EGR valve.  So does that still sound like a temp sensor and if so where is that located on the car so I can change it.
Thank you so much again for your knowledge

Answer
As long as the EGR issue was fixed and the lamp isn't coming on, I doubt your current problem is related.

I'm hard-pressed to say I think the sensor will fix the issue, but it's also my best guess at this point.  

The sensor screws into the front of the coolant housing on the transmission end of the engine.  (Sorry.  I should have included that in the previous answer.)