W126 Water Temp sensor location
 

Iv'e searched but somwwhat confused. 380SE just started to exhibit rough idle when first started cold. Starts ok but sounds like it is stumbling. Goes away after driving for about a mile, and is smooth as ever when warmed up or even before temp gauge gets to 80C. Saw others comments that this may be due to faulty water temp sensor among other possibilities. Where exactly is this part located( off the thermostat housing?). Vacuum lines are fine, new plugs, dist cap, rotor. Problem only exits when I first start it up.

I guess it's your smog pump that is working properly.

rough cold idle on 380SEL
 

Generally, a rough idle only when cold is either a vacuum leak (around the fuel injector seal(s)) or faulty fuel delivery--poor injector spray pattern, partially plugged, defective fuel distributor--in increasing cost to fix order.
1) check for vacuum leaks around injector seals by dribbling a water hose on the injectors when you first start the car--if one is leaking, you will hear the 'sucking sound' and a misfire will happen when the water gets sucked in.
2) Run a can of BG-44 fuel injector cleaner to try and clean up the injectors. 3)If you have not been running a 'clean-up' quality gasoline--run abig bottle of TECHRON through system to remove gum deposits from the intake vlaves. It only takes a little crud to soak up the tiny amount of fuel sprayed in at idle and lean out the mixture enough to cause a misfire.
4) Fuel distributor mal-function (damage from rust or debris) would generally show up all the time and a failed diaphraghm in the fuel distributor would cause 'flooded' hot starts and a rich idle.

Post-1980 116 engines.

thanks donbryce