Actually sounds more like engine from the added description, that's why Marde asked for additional details.
Engine idles higher when cold, at it's lowest RPM warm. You'll have to add engine type for specific info., can't guess which is in hers.
General comments, The IAC could be responding poorly at low rpm to compensate for the trans load - could be a "tune-up" issue just needing maint. for poor operation at idle - the mounts Marde mentioned could be involved - list goes on.
That'll give you some ideas, folks can guess more with additional input.