DIAGNOSIS That's likely the internal cooling fan running. The camera has a small fan to keep its electronics from overheating, and sometimes you can hear it spin up, especially if it's in a warm spot or has been streaming for a long time.
FIX First, check the camera's environment. 1) Make sure it's not sitting right on top of a radiator, in direct sunlight, or crammed in an entertainment center with other hot electronics. 2) Give it a few inches of clearance on all sides, especially the back where the vents are, for proper airflow. A cooler camera won't need the fan to run as hard or as often.
IF THAT DIDN'T WORK If the sound is more of a rapid clicking or grinding, it could be a faulty fan bearing. Unfortunately, there's no user-serviceable fix for that. If the camera is still under warranty, contact Google support.
HEADS UP Hearing the fan occasionally is normal. But if the sound is new, very loud, or the camera feels hot to the touch, unplug it and let it cool down to prevent any potential damage.