Customer of mine has an issue with the fan running constantly in his NX9420 HP Compaq notebook. This only happens when the AC power adapter is plugged in.
Eventually I determined this:
The notebook is an older model. The fan is starting to wear and thus the fan noise is more apparent. The fan has always been running, it's just louder and thus more noticeable than before.
The GPU video adapter draws full power even when idle. The system board sees this and the associated heat and trips the fan.
There is a BIOS setting that disables turning on the fan when connected to AC power. Unfortunately, it has no effect whatsoever.