Others have said that the IAC can make a difference but it really shouldn't and I haven't seen that, maybe they could chime in more on that. I've never heard the throttle body causing that issue but you never know, maybe more likely than the IAC motor ?? What happens when you clear the DME adaptations ??

If you don't know the history it is possible that someone has used carb cleaner to clean the throttle body which could for sure cause it to react slower as the o-rings swell and drag. I would eliminate as much as you can first though.

__________________
1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)