What we found
An intermittent fault that clears itself is the hardest kind to pin down, because by the time the vehicle reaches the shop it is usually behaving. We left it overnight so we could see it cold in the morning.
On start-up the misfire was clear on cylinder 3. Live data showed short-term fuel trim swinging positive at idle and settling once the engine warmed, which points at unmetered air getting in rather than a fuelling problem. A smoke test found it: a hairline split in the intake boot that opened up when the rubber was cold and stiff, and sealed as it warmed and softened.
That is why the symptom disappeared after a minute, and why no code ever set — the engine compensated fast enough to stay inside tolerance.
What we did
Replaced the intake boot with an OE part. Cleaned the throttle body while it was open, since it was accessible and carbon build-up was contributing to the rough idle. Cleared adaptives and let the engine relearn.
How it turned out
Started clean the following morning from cold. Fuel trims held steady. The customer reported no recurrence over the following weeks.
A fault that only appears cold is telling you something about temperature and materials. Chasing it warm wastes everyone's time — leave the vehicle overnight.
Prices and times are what this job took on this vehicle. Yours may differ — we will tell you before we start, not after.