1998 318i SE Idling Problem

Hi everybody, I'm new here.

I drive a lovely 1998 alpine white e36 318i SE. It has a
small problem with the way it idles. It seems to run a
little rich when cold and when driving, when the engine
returns to idle (e.g. coasting up to traffic lights
clutch down) the revs drop very very low and the engine
almost stops but then seems to rescue itself and returns
to a normal idle.

The problem seems to occur mainly in COLD weather. I have
checked for air leaks, changed the plugs and serviced it
and checked the air filter. Any ideas as to the nature of
the fault? I'm thinking coolant temperature sensor, does
that seem sensible?

Edited by sc318