As the camera warms up and approaches the temperature just before the fan kicks on full (hopefully, with the fan set 25-45%), I'm curious if the noise levels change?

I would guess it generates more heat when recording, or at least this should be the case when the energy management features are implemented. So that, even if you keep the camera turned on, the internal temperature can change while recording?

Has any testing been done when recording at 320/800 to see how much noise is introduced when the camera is at certain internal temperature ranges of plus and minus that are different from the temperature at which it was black shaded?