Could be an injector that starts to leak. This will happen only when the engine reaches a certain temperature. It probably relates to the A/C only because when the A/C is on, the engine is a tad hotter, but the dual temp sensor does not read the temp at the heads.
try to PM Fmugur. he had a similar issue, and it could not be solved by reading GT1 or INPA. He had his car tested at some very specialized shops, and they couldn't figure it out. He somehow caught it though, and it was 1 or 2 leaking injectors (as I said - they will leak, once the temp reaches a certain value - not sure what this value is). He also had no stutter, etc. He also had to let the car cool down, then it would start OK.

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Stable: e92is, e46 M54B25, e83 N52, e53 N62 - sold, e39 M54B30 R.I.P.