91 525i Engine Stutter and Hesitatation

[DynoDuckfart]

Hey there Gurus,

I have searched all 39 pages in hopes to avoid a repost and maybe I missed the answer to my question.
I have a '91 525i that has been giving a few probs... It has 267k miles on it. Alot I know, but, knowing the cars rep, it should continue for as long as I have the cash to put into it.
This winter here in Michigan, I noticed a change in how she runs.
When I first start it up, it runs perfect. After it warms up a bit, it begins to hesitate and stutter when I press the accelerator. I was worried about the timing being off. (I have a NOS system in one of my other cars and the problem resembled a similar situation when I set the timing a few degrees off as to get the NOS to work properly.)
This problem only surfaces when I accelerate more aggresively, i.e passing another car, entering on a highway, taking off from a stop. etc.
When I press the accelerator slowly, it doesn't do this stutter as much.
I've swaped out the plugs starting small, ran injector cleaner through, and performed the regular maintaince on the KN filter.
I've known the car since it was new. It's on it's 2nd timing belt. So, that's not the issue.
I'm told that there are 2 sensors attached to the thermostat...? Welp, I dunno. The last Bimmer I owned was a 77 630CSI... Totaled by another driver. And with this one, I am at a loss.
I baught it from my childhood friends father for an excellent price, (1500 bucks) It's spotless and looks good. But runs a bit rough.
Any ideas from a Guru on this one?
Thank you in advance. And I appologize if I have reposted this question.

[DynoDuckfart]

Anybody have an idea.....?