My 2004 350Z Roadster with a gearbox and 60K miles makes a loud, low pitch moan when driving in the first ten minutes on the road in cold weather.
The sound completely disappears after about ten minutes and the car drives just fine. A smoke test shows no vacuum leak. The noise appears only under load.
Revving the car in neutral does not produce the sound. The car is at my mechanic for an early morning check ride. Any ideas are welcome.;

 

If it makes a noise under load in gear but nothing when revving it in neutral, then it sounds related to the gearbox/transmission as opposed to the engine.

Noises are hard to diagnose over the Internet. Definitely report back what your mechanic says.

Original transmission fluid and other transmission components?

 

Tranny oil is 75/90 Red Line. The noise was there before and after the switch from OEM oil. I like your thinking though, but where does cold
weather fit in at the start? The sound never occurs above 50 F. My mechanic owns a magic wand. Let's see what he discovers.