Loud fan with low CPU

I understand your Mac's cooling fans become objectionably loud on occasion, and you are unable to correlate that behaviour to any particular app or process.

For reference, read About fans and fan noise in your Apple product - Apple Support, in which you will eventually find this passage from Keep your Mac laptop within acceptable operating temperatures - Apple Support:

"If your Mac laptop gets warm even when it isn’t doing tasks that require intensive calculations, or if it has fans that run for a long time, use Activity Monitor to check CPU activity. Look for malfunctioning processes that can put a significant load on the CPU and check for unexpected fan use. If issues persist, close and open the lid on your laptop, or restart your computer. ..."

Run Apple Diagnostics, which will exercise the fan and test that Mac's thermal sensors: Use Apple Diagnostics to test your Mac - Apple Support. Since the problem is sporadic Apple Diagnostics is very likely to conclude "no trouble found" but if it identifies a specific fault, that would be considered a conclusive outcome.

Post a screenshot of Activity Monitor if you wish. Use the Energy pane, or CPU sorted by %CPU to see which apps or processes are using the most energy or are placing the greatest demands on your Mac's CPU when the fans start to become audible. To show the most relevant information I suggest selecting "Active Processes" from Activity Monitor's View menu.

To take a screenshot read Take a screenshot on your Mac - Apple Support. To post it in a reply use the "Image insertion" icon pictured below:

Finally, if nothing helps please write back for additional suggestions.

I've found some circumstances lately where some processes not flagged as "active" yet were contributing to the workload. You might try changing the View setting the "All Processes and see if any new "hungry hippos" show up.

In the two+ decads I've been here, I've seen enough grief form a premature OS update that I now recommend updating the OS only AFTER the bugs have ben fully evaluated or noting else works. That is selsom a fix unless Apple says there is a know bug in the previous OS version.

Right now it looks like your bug is wearing a Google shirt.

Google Mail is clearly using an inordinate amount of CPU. Is that unexpected?

Sonoma 14.1.2 is now out, maybe updating might clear your problem.