Remove (or throttle) fan on eMac
If you fan is making enough noise to give you a headache it's because the bearing has worn out.  

Removing the fan is not a good idea.  Fans in computers either pull in cool air or expel warm air.  The fact that this fan was close to the drive doesn't negate the fact that it wasn't displacing the "other" warm ambient air around the drive.

You have three options:


Replace the fan.  A quick search on eBay shows there are still fans available for the eMac.
Replace the motor.  The good news is that the fan motor and blades aren't so custom as you would think.  The fan PN# is 4710KL-04W-B56 and can also be found on eBay quite easily.  You can disassemble the fan, extract the motor/blades and replace it.
Replace the bearing.  These older fan assemblies could actually be taken apart (if you're careful).  Simply replace the bearing assembly (you'll need ID and OD measurements) and purchase a bearing online.